We study the role that the axiom of choice plays in Tychonoff's product theorem restricted to countable families of compact, as well as, Lindelöf metric spaces, and in disjoint topological unions of countably many such spaces.

This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We illustrate this interplay by proving that in the Laver model for the consistency of the Borel’s conjecture, the product of any two metrizable spaces with the Hurewicz property has the Menger property.

The 2023 edition of the Venice Architecture Biennial Time Space Existence will draw attention to the emerging expressions of sustainability in their numerous forms, ranging from a focus on the environment and urban landscape to the unfolding conversations on innovation, reuse, community, and inclusion. In response to climate change, exhibited projects will investigate new technologies and construction methods that reduce energy consumption through circular design and develop innovative, organic, and recycled building materials. Participants will also address social justice by presenting (...) living solutions envisioned for displaced communities and minorities, while others will examine the tensions between the built urban environment and the nature surrounding it, identifying opportunities for coexistence. Time Space Existence not only aims to be a display but also a living workshop where established and emerging practitioners can work together and present their own visions of the status of architecture and the built environment nowadays. By bringing together ideas from across the world, the exhibition presents itself as a platform for exchange and experimentation and strives to stimulate an engaging dialogue that is inclusive of all voices. (shrink)

This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.

We study the Tychonoff Compactness Theorem for several different definitions of a compact space.

We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a separable metrizable space. Our techniques employ deep results from effective descriptive set theory and recursion theory. In fact it is essential to extend several prominent results in recursion theory (e.g. the Shore-Slaman Join Theorem) to the setting of Polish spaces. As a by-product we give both positive and negative (...) results on the Martin Conjecture on the degree preserving Borel functions between Polish spaces. Additionally we prove results about the transfinite version as well as the computable version of the Decomposability Conjecture. (shrink)

The category of Scott-domains gives a computability theory for possibly uncountable topological spaces, via representations. In particular, every separable Banach-space is representable over a separable domain. A large class of topological spaces, including all Banach-spaces, is representable by domains, and in domain theory, there is a well-understood notion of parametrizations over a domain. We explore the link with parameter-dependent collections of spaces in e. g. functional analysis through a case study of "Lp" -spaces. We show (...) that a well-known domain representation of "Lp" as a metric space can be made uniform in the sense of parametrizations of domains. The uniform representations admit lifting of continuous functions and are effective in p. Dependent type constructions apply, and through the study of the sum and product spaces, we clarify the notions of uniformity and uniform computability. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

Let {: i ∈I } be a family of compact spaces and let X be their Tychonoff product. [MATHEMATICAL SCRIPT CAPITAL C] denotes the family of all basic non-trivial closed subsets of X and [MATHEMATICAL SCRIPT CAPITAL C]R denotes the family of all closed subsets H = V × Πmath imageXi of X, where V is a non-trivial closed subset of Πmath imageXi and QH is a finite non-empty subset of I. We show: Every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT (...) CAPITAL C]R extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ if and only if every family H ⊂ [MATHEMATICAL SCRIPT CAPITAL C] with the finite intersection property extends to a maximal [MATHEMATICAL SCRIPT CAPITAL C] family F with the fip. The proposition “if every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ, then X is compact” is not provable in ZF. The statement “for every family {: i ∈ I } of compact spaces, every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R, Y = Πi ∈IYi, extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ” is equivalent to Tychonoff's compactness theorem. The statement “for every family {: i ∈ ω } of compact spaces, every countable filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R, X = Πi ∈ωXi, extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ” is equivalent to Tychonoff's compactness theorem restricted to countable families. The countable Axiom of Choice is equivalent to the proposition “for every family {: i ∈ ω } of compact topological spaces, every countable family ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C] with the fip extends to a maximal [MATHEMATICAL SCRIPT CAPITAL C] family ℱ with the fip”. (shrink)

This paper argues against evolutionary accounts of aesthetics by defending the idea that our fundamental aesthetic categories have undergone great changes in the last two millennia, in particular, during an “artistic revolution” that lasted from 1680 to 1830. This revolution was made possible by the development of a number of technologies of art that created a separate cultural space for this new invention. The attempt to extend this revolution to include the aesthetic appreciation of the natural environment is aided by (...) a new set of technologies that help make an aesthetic object out of natural environments. This even morerecent development is further evidence against an evolutionary explanation of art. (shrink)

In Geography and the Production of Space in Nineteenth-Century American Literature, Hsuan L. Hsu examines how literature represents different kinds of spaces ranging from the single-family home to the globe. He focuses on authors such as Charles Brockden Brown, Edgar Allan Poe, Herman Melville and Sarah Orne Jewett, who drew on literary tools such as rhetoric, setting, and point of view to mediate between individuals and different kinds of spaces. These authors used forms such as the regional sketch, (...) the domestic novel, and the detective story to re-examine how local spaces and communities would change when incorporated into global economic and political networks. Geography and the Production of Space in Nineteenth-Century American Literature is valuable reading for American literature scholars, and for all concerned with intersections between literature and geography"--Provided by publisher. (shrink)

How can performance transform places of urban renewal and regeneration? What does performance contribute to the creation of community? These are some of the questions addressed in this study of the relationship of performance to urban space. Marrying theory with a series of international case studies of performance practice and interviews with practitioners, this interdisciplinary study examines how space is performatively produced to create a sense of 'placeness'. Case studies are drawn from Canada, Brazil, the Czech Republic, the UK and (...) Spain. (shrink)

John Damascene, one of the most productive Greek theologians of the Middle Byzantine era, also composed a treatise on the Trisagion hymn, or how it should be sung correctly and why; a text that has been little discussed in contemporary scholarship. The present paper provides an overview of the work – with special reference to the notion of identity in John’s description of the Trinitarian doctrine. It also examines the treatise especially in the context of anti-heretical polemics. The author argues (...) that John’s approach to the question of the correct way of singing the hymn is gentle: instead of using pejorative language, he even praises the object of his reproach. (shrink)

A notion of factorizability for vector-valued measures on a quantum logic L enables us to pass from abstract logics to Hilbert space logics and thereby to construct tensor products. A claim by Kruszynski that, in effect, every orthogonally scattered measure is factorizable is shown to be false. Some criteria for factorizability are found.

Henri Lefebvre has considerable claims to be the greatest living philosopher. His work spans some sixty years and includes original work on a diverse range of subjects, from dialectical materialism to architecture, urbanism and the experience of everyday life. The Production of Space is his major philosophical work and its translation has been long awaited by scholars in many different fields. The book is a search for a reconciliation between mental space and real space. In the course of his exploration, (...) Henri Lefebvre moves from metaphysical and ideological considerations of the meaning of space to its experience in the everyday life of home and city. He seeks, in other words, to bridge the gap between the realms of theory and practice, between the mental and the social, and between philosophy and reality. In doing so, he ranges through art, literature, architecture and economics, and further provides a powerful antidote to the sterile and obfuscatory methods and theories characteristic of much recent continental philosophy. This is a work of great vision and incisiveness. It is also characterized by its author's wit and by anecdote, as well as by a deftness of style which Donald Nicholson-Smith's sensitive translation precisely captures. (shrink)

Landscape and brandingexplores the way landscape is conceptualised, conceived, represented and designed by professionals in a brand-driven age. Landscape - incorporating tangible physical space as well as intangible concepts, narratives, images, and experiences of place - is constructed by a number of creative industries. This book tests the hypothesis that place branding, a powerful marketing and management practice, increasingly blurs the distinction between the promotionof landscape and its production in design terms. Place branding involves the strategic and systematic composition of (...) single-minded, experiential and market-friendly place identities which are consistently communicated across various media, including physical space. How does this implicate or transform notions of place, nature, landscape experience, and the qualitative value of landscape itself? How does this affect the role of landscape architecture? To answer these questions, place branding theory and practice is critically examined alongside an in depth case study of one specific landscape - the Blue Mountains (Australia). Projects undertaken between 1995 and 2015, including a branding strategy for the region, media campaigns, television, cinema, and several landscape architectural works in the public and private domain are comparatively analysed, focusing on the discourse, conventions and values informing their production, and the landscape narratives they convey. (shrink)

We establish the following results: 1. In ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC), for every set I and for every ordinal number α ≥ ω, the following statements are equivalent: (a) The Tychonoff product of| α| many non-empty finite discrete subsets of I is compact. (b) The union of| α| many non-empty finite subsets of I is well orderable. 2. The statement: For every infinite set I, every closed subset of the Tychonoff product [0, 1] (...) I which consists of functions with finite support is compact, is not provable in ZF set theory. 3. The statement: For every set I, the principle of dependent choices relativised to I implies the Tychonoff product of countably many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰ (i.e., ZF minus the Axiom of Regularity). 4. The statement: For every set I, every ℵ₀-sized family of non-empty finite subsets of I has a choice function implies the Tychonoff product of ℵ₀ many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰. (shrink)

Philosophers and geographers have converged on the topic of public space, fascinated and in many ways alarmed by fundamental changes in the way post-industrial societies produce space for public use, and in the way citizens of these same societies perceive and constitute themselves as a public. This volume advances this inquiry, making extensive use of political and social theory, while drawing intimate connections between political principles, social processes, and the commonplaces of our everyday environments.

Philosophers and geographers have converged on the topic of public space, fascinated and in many ways alarmed by fundamental changes in the way post-industrial societies produce space for public use, and in the way citizens of these same societies perceive and constitute themselves as a public. This volume advances this inquiry, making extensive use of political and social theory, while drawing intimate connections between political principles, social processes, and the commonplaces of our everyday environments.

Philosophers and geographers have converged on the topic of public space, fascinated and in many ways alarmed by fundamental changes in the way post-industrial societies produce space for public use, and in the way citizens of these same societies perceive and constitute themselves as a public. This volume advances this inquiry, making extensive use of political and social theory, while drawing intimate connections between political principles, social processes, and the commonplaces of our everyday environments.

An important part of the world we live in is represented by symbols, and mediated images and mass media are the main sources of the symbolic material used in the process of shaping the postmodern self. The cultural industry and the communication technology are growing rapidly and they capture important areas located until recently under the tutelage of traditional social institutions such as the family or the church. If we think of the contemporary society in terms of the weak theology (...) proposed by John D. Caputo as a de-secularized space where the individual’s need for the sacred is strongly revealed, the crucial role played by the media in the construction of the contemporary world becomes obvious. Certainly, within this vast territory represented by the media culture, advertising is one of the most relevant areas for analysis of the manner in which symbolic structures are reintegrated in contemporary society. Therefore, our paper focuses on advertising as an important force that creates symbolic meanings in the contemporary culture. Along with the symbolic content of advertising, a significant part in augmenting its cultural force is attributed to the way it succeeds to contain religious dimensions in its mechanisms. (shrink)

This essay applies Henri Lefebvre’s notion of the production of space, particularly his conceptualization of the tension formed by the perceived-conceived-lived triad to analyze how space is produced in wartime hospitals as demonstrated in Richard Selzer’s “The Whistlers’ Room.” Wounded soldiers participate in producing the triad of the social space of military hospitals through their multilayered performances as fighting soldiers serving the nation and as living human beings longing for human connections. Contradictory performances demonstrate the strategic positioning of wounded soldiers (...) as active producers of different social spaces. By representing the lived spaces produced by wounded soldiers, Selzer challenges the hegemonic representations of the conceived spaces of military hospitals. Selzer’s exploration of soldiers’ contradictory performances opens up opportunities for discussion of writing physicians who assume a similar role by positioning themselves strategically within the medical institution. (shrink)

It is shown that the product of finitely many sequential, CLP-compact spaces is CLP-compact.

For any unit vector in an inner product space S, we define a mapping on the system of all ⊥-closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. (...) Finally, the result will be generalized to general inner product spaces. (shrink)

Francis Fukuyama postulated that there are two powerful forces at work in human history. One, he calls, ‘the logic of modern science’ and the other, ‘the struggle for recognition’. I agree with Fukuyama that human developmental progression is propelled by these twin principles. It is my position that these principles have been the drivers of geopolitics. In this paper, I argue that, in addition, knowledge production is a major factor in geopolitics and that the Euro-American worldview has occupied the place (...) of hegemony by reason of knowledge production. Africa has been denied having any form of epistemic tradition by the Euro-American world to sustain itself in the position of hegemony. In the era of Fourth Industrial Revolution, it will be antithetical for Africa to continue to adopt or consume technologies driven by Eurocentrism without projecting its contribution to the global space. Hence, using a critical hermeneutical approach, I contend that Africa needs to make a unique African contribution in the era of Fourth Industrial Revolution. It is Africa’s unique contribution that will guarantee Africa a place in geopolitics. (shrink)

In the topological semantics, quantified intuitionistic logic, QH, is known to be strongly complete not only for the class of all topological spaces but also for some particular topological spaces — for example, for the irrational line, ${\Bbb P}$, and for the rational line, ${\Bbb Q}$, in each case with a constant countable domain for the quantifiers. Each of ${\Bbb P}$ and ${\Bbb Q}$ is a separable zero-dimensional dense-in-itself metrizable space. The main result of the current article (...) generalizes these known results: QH is strongly complete for any zero-dimensional dense-in-itself metrizable space with a constant domain of cardinality ≤ the space’s weight; consequently, QH is strongly complete for any separable zero-dimensional dense-in-itself metrizable space with a constant countable domain. We also prove a result that follows from earlier work of Moerdijk: if we allow varying domains for the quantifiers, then QH is strongly complete for any dense-in-itself metrizable space with countable domains. (shrink)

We investigate in ZF conditions that are necessary and sufficient for countable products ∏m∈ℕXm of finite Hausdorff spaces Xm resp. Hausdorff spaces Xm with at most n points to be compact resp. Baire. Typica results: Countable products of finite Hausdorff spaces are compact if and only if countable products of non-empty finite sets are non-empty. Countable products of discrete spaces with at most n + 1 points are compact if and only if (...) countable products of non-empty sets with at most n points are non-empty. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:36 Feminist Studies 45, no. 1. © 2019 by Feminist Studies, Inc. Sonny Nordmarken Queering Gendering: Trans Epistemologies and the Disruption and Production of Gender Accomplishment Practices Those who are deemed “unreal” nevertheless lay hold of the real, a laying hold that happens in concert, and a vital instability is produced by that performative surprise. —Judith Butler, Gender Trouble Beginning in the 1960s, scholars began to theorize gender as (...) a contextually specific process rather than a universal category reflecting an essential pre-discursive sex. Two interrelated traditions developed: a discursive approach, which theorized gender as performative, and an interactionist approach, which investigated the interactional achievement of gender. For Judith Butler, “what we take to be an internal essence of gender is manufactured through a sustained set of acts, posited through the gendered stylization of the body.”1 Gender is therefore performative : it is a series of effects produced through the repetition and citation of stylized acts, which are named via and thus produced through discourse ; discourse also produces the defining limits of subjects.2 Candace West and Don Zimmerman theorized gender as a “routine, methodical, 1. Judith Butler, Gender Trouble, 10th anniversary ed. (New York: Routledge, 1999), xv. 2. Butler, Gender Trouble; Judith Butler, Bodies that Matter: On the Discursive Limits of Sex (New York: Routledge, 1993); Judith Butler, Undoing Gender (New York: Routledge, 2004). Sonny Nordmarken 37 and recurring accomplishment” produced in social interaction.3 They observed how, in the relational process of “doing gender,” social actors display gender, presenting an appearance to others, who attribute gender by interpreting this appearance. In this article, I investigate how actors interactionally challenge and construct discursive structures in order to contribute to scholarship that analyzes the role language plays in such interactions.4 Following Sandy Stone, who suggests that transsexuals are not a class, nor a third gender, but a genre, “a set of embodied texts,” who, through their interpretation, might potentially disrupt dichotomous sexuality and gender categories, I examine the spaces in which the discursive and the interactional merge to investigate how gender minorities, as simultaneous subjects, texts, social actors, and cultural workers, queer hegemonic gender practices.5 I argue that members of trans linguistic communities and gender nonconforming individuals queer the normative gender process in two ways: by productively linguistically communicating third-person gender pronouns and by disruptively inhibiting gender’s hegemonic attribution. Lal Zimman has made parallel observations, explaining linguistic gender self-determination practices as a new cultural phenomenon, focusing on terminology for types of gendered persons, grammatical gender forms (i.e., pronouns), and lexical items that relate to embodied sex.6 My analysis builds on Zimman’s observations using sociological, performance 3. Candace West and Don H. Zimmerman, “Doing Gender,” Gender & Society 1, no. 2 (1987): 126. 4. For example, see Mimi Schippers, “Recovering the Feminine Other: Masculinity, Femininity, and Gender Hegemony,” Theory and Society 36, no. 1 (2007): 85–102. 5. Sandy Stone, “The Empire Strikes Back: A Posttranssexual Manifesto,” in Body Guards: The Cultural Politics of Gender Ambiguity, ed. Julia Epstein and Kristina Straub (New York: Routledge, 1991), 296. The term “gender minorities ” encompasses individuals identifying with gender identity terms other than those they were assigned and individuals with gender nonconforming appearance. 6. See Lal Zimman, “Transgender Language Reform: Some Challenges and Strategies for Promoting Trans-affirming, Gender-Inclusive Language,” Journal of Language and Discrimination 1, no. 1 (2017): 84–105; Lal Zimman, “Trans People’s Linguistic Self-Determination and the Dialogic Nature of Identity,” in Representing Trans: Linguistic, Legal, and Everyday Perspectives, ed. Evan Hazenberg and Miriam Meyerhoff (Wellington, New Zealand: Victoria University Press, 2017). 38 Sonny Nordmarken studies and performativity frameworks to theorize these practices. By approximating new gender pronoun-attribution norms that bring a trans queer paradigm to life in interactions and by disregarding their perceptions of each other’s bodies, actors accomplish gender pronouns linguistically, override hegemonic gender attribution norms, and reorganize gender accountability. These practices institutionalize a new interpretive frame and accountability structure through which social actors create and recognize a variety of gender expressions, identities, and pronouns, reworking performativity to produce gender minorities as subjects. I argue that this gendering-queering is a form of disidentificatory gender accomplishment. In addition, I... (shrink)

Recent discussions of human categories have suffered from an over emphasis on intention and language, and have not paid enough attention to the role of material conditions, and, specifically, of social space in the construction of human categories. The relationship between human categories and social spaces is vital, especially with the categories of class, race, and gender. This paper argues that social space is not merely the consequent of the division of the world into social categories; it is constitutive (...) of social categories. To put it more bluntly, if who we are is bound up with place, then not only do we inhabit a divided America; divided America inhabits us. The second, and equally dramatic, conclusion is that attempts to transform social categories must involve the transformation of social space. When we sort people by categories, we do so spatially: with race come racialized spaces. And because our place comes to inhabit us, when we divide spatially we cannot help but to inscribe and produce categories and identities associated with our spatial divisions: with racialized spaces come race. Recognition of this dialectic is a direct challenge to the one-way considerations of social identity and social space that occurs in much urban sociology and history. Moreover, it demonstrates that there is an internal contradiction in policies--often based in urban sociology and history--that assume that integration can be accomplished along with the conservation of ethnic and racial identity. (shrink)

A lump theorist claims that ordinary objects are spread out across possible worlds, much like many of us think that tables are spread out across space. We are not wholly located in any one particular world, the lump theorist claims, just as we are not wholly spatially located where one’s hand is. We are modally spread out, a trans-world mereological sum of world-bound parts. We are lump sums of modal parts. And so are all other ordinary objects. In this (...) paper, I explore lump theory and investigate five arguments against it. These arguments may be the primary reasons why lump theory has not been widely accepted––or extensively explored––until now. I maintain that these arguments can be answered, and moreover, that accepting lump theory has distinct advantages, making it a competitive view in its own right. (shrink)

We announce two new dichotomy theorems for Borel equivalence relations, and present the results in context by giving an overview of related recent developments.§1. Introduction. For X a Polish space and E a Borel equivalence relation on X, a classification of X up to E-equivalence consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c = c. To be of any value we would expect I and c to be (...) “explicit” or “definable”. The theory of Borel equivalence relations investigates the nature of possible invariants and provides a hierarchy of notions of classification.The following partial ordering is fundamental in organizing this study. Given equivalence relations E and F on X and Y, resp., we say that E can be Borel reduced to F, in symbolsif there is a Borel map f : X → Y with xEy ⇔ fFf. Then if is an embedding of X/E into Y/F, which is “Borel”.Intuitively, E ≤BF might be interpreted in any one of the following ways: The classi.cation problem for E is simpler than that of F: any invariants for F work as well for E. One can classify E by using as invariants F-equivalence classes. The quotient space X/E has “Borel cardinality” less than or equal to that of Y/F, in the sense that there is a “Borel” embedding of X/E into Y/F. (shrink)

Introduction -- Henri Lefebvre : the production of theory -- Research : from practices of dwelling to the production of space -- Critique : space as concrete abstraction -- Project : urban society and its architecture -- Afterword : toward an architecture of jouissance.

In this paper, we argue that nurses need to be aware of how the production of space in specific contexts – including health care systems and research institutions – perpetuates marginalized populations' state of social otherness. Lefebvre's idea regarding spatial triad is mobilized in this paper, as it pertains to two‐spirited, lesbian, gay, bisexual, trans and queer populations (2SLGBTQ*). We believe that nurses can create counter‐spaces within health care systems and research institutions that challenge normative discourses. Lefebvre's work provides (...) us the necessary tools to understand how various places or environments produce identities. In understanding Lefebvre's principles, we believe that nurses can play an essential role in creating counter‐spaces, thereby instigating counter‐institutional practices, for those who experience otherness. (shrink)

The automorphism groups of scalar products of spinors are determined. Spinors are considered as elements of minimal left ideals of Clifford algebras on quadratic modules, e.g., on orthogonal spaces. Orthogonal spaces of any dimension and arbitrary signature are discussed. For example, the automorphism groups of scalar products of Pauli spinors and Dirac spinors are, respectively, isomorphic to the matrix groups U(2) and U(2, 2). It is found that there are, in general, 32 different types or similarity (...) classes of such automorphism groups, if one considers real orthogonal spaces of arbitrary dimension and arbitrary signature. On a more abstract level this means that the Brauer-Wall group of the real field R, consisting of graded central simple algebras over R, can be extended from the cyclic group of 8 elements to an abelian group with32 elements. This extended Brauer-Wall group is seen to be isomorphic with the group (Z 8 × Z 8 )/Z 2 and it consists of real Clifford algebras with antiinvolutions. Moreover, the subgroup determined by the antiinvolution is isomorphic to the automorphism group of scalar products of spinors. (shrink)

Techniques for constructing the tensor product of two generalized sample spaces which admit unital sets of dispersion-free weights are discussed. A duality theory is developed, based on the 1-cuts of the dispersion-free weights, and used to produce a candidate for the tensor product. This construction is verified for Dacification manuals, a conjecture is given for other reflexive cases, and some adjustments for nonreflexive cases are considered. An alternate approach, using graphs of interpretation morphisms on the duals, is also presented.

This article examines recent practices of landscape photography in light of Henri Lefebvre's influential theorisation of the production of space. The abiding value of Lefebvre's analysis for our understanding of social geography and contemporary Capitalism is elaborated through discussion of selected photographic works that, in different ways, each foreground the socio-hisotrically constructed character of space. This analysis enables the rearticulation of Lefebvre's influential analysis of space in light of later artistic practices and in relation to subsequent developments in the form (...) of Capitalism. (shrink)