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  1. Peter Aczel (2006). Aspects of General Topology in Constructive Set Theory. Annals of Pure and Applied Logic 137 (1):3-29.
    Working in constructive set theory we formulate notions of constructive topological space and set-generated locale so as to get a good constructive general version of the classical Galois adjunction between topological spaces and locales. Our notion of constructive topological space allows for the space to have a class of points that need not be a set. Also our notion of locale allows the locale to have a class of elements that need not be a set. Class sized mathematical structures need (...)
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  2. Peter Aczel & Giovanni Curi (2010). On the T1 Axiom and Other Separation Properties in Constructive Point-Free and Point-Set Topology. Annals of Pure and Applied Logic 161 (4):560-569.
    In this note a T1 formal space is a formal space whose points are closed as subspaces. Any regular formal space is T1. We introduce the more general notion of a formal space, and prove that the class of points of a weakly set-presentable formal space is a set in the constructive set theory CZF. The same also holds in constructive type theory. We then formulate separation properties for constructive topological spaces , strengthening separation properties discussed elsewhere. Finally we relate (...)
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  3. Ernest W. Adams (1996). Topology, Empiricism, and Operationalism. The Monist 79 (1):1--20.
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  4. Frank Arntzenius (2008). Gunk, Topology and Measure. In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4. Oup Oxford.
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  5. Steve Awodey (2008). Topology and Modality: The Topological Interpretation of First-Order Modal Logic: Topology and Modality. Review of Symbolic Logic 1 (2):146-166.
    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.
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  6. Steve Awody & K. Kishida (2008). Topology and Modality: The Topological Interpretation of First-Order Modal Logic. Review of Symbolic Logic 1 (2):146-166.
    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.
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  7. Nils A. Baas (2009). Hyperstructures, Topology and Datasets. Axiomathes 19 (3):281-295.
    In the natural sciences higher order structures often occur. There seems to be a need for good methods of describing what we mean by higher order structures in various contexts. This is what hyperstructures are intended to do. We motivate and introduce this new concept. Next we illustrate how it can be applied in various types of genomic analysis—particular the correlations between single nucleotide polymorphisms and diseases. The suggested structure is quite general and may be applied to a variety of (...)
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  8. Babette Babich, Heidegger's Silence: Towards a Post-Modern Topology.
    in Charles Scott and Arleen Dallery, eds., Ethics and Danger: Currents in Continental Thought. Albany. State University of New York Press. 1992. Pp. 83-106.
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  9. Roxana Baiasu (2009). Heidegger's Topology: Being, Place, World, by Jeff Malpas. European Journal of Philosophy 17 (2):315-323.
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  10. Paul Bankston (1984). Expressive Power in First Order Topology. Journal of Symbolic Logic 49 (2):478-487.
    A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and (...)
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  11. Jason Barker (2003). The Topology of Revolution. Communication and Cognition. Monographies 36 (1-2):61-72.
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  12. Alessandro Berarducci, Mário Edmundo & Margarita Otero (2007). Corrigendum To: "Transfer Methods for O-Minimal Topology". Journal of Symbolic Logic 72 (3):1079 - 1080.
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  13. Alessandro Berarducci & Margarita Otero (2003). Transfer Methods for o-Minimal Topology. Journal of Symbolic Logic 68 (3):785-794.
    Let M be an o-minimal expansion of an ordered field. Let φ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from $\varphi^M$ to $\varphi^R$ and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo-based on the work of A. Strzebonski-showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.
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  14. Erhard Bieberich, Structure in Human Consciousness: A Fractal Approach to the Topology of the Self Perceiving an Outer World in an Inner Space.
    In human consciousness a world of separated objects is perceived by an inner observer who is experienced as an undivided feeling of one-self. A topological correlation of the self to the world, however, entails a paradoxical situation by either merging all separated objects into one or splitting the self into as many subselves as there are objects perceived. This study introduces a model suggesting that the self is generated in a neural network by algorithmic compression of spatial and temporal information (...)
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  15. David Bohm (1962). Classical and Non-Classical Concepts in the Quantum Theory. British Journal for the Philosophy of Science 12 (48):265-280.
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  16. Giovanni Boniolo & Silvio Valentini (2008). Vagueness, Kant and Topology: A Study of Formal Epistemology. Journal of Philosophical Logic 37 (2):141 - 168.
    In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.
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  17. Dan Braha & Yaneer Bar-Yam, Topology of Large-Scale Engineering Problem-Solving Networks.
    The last few years have led to a series of discoveries that uncovered statistical properties that are common to a variety of diverse real-world social, information, biological, and technological networks. The goal of the present paper is to investigate the statistical properties of networks of people engaged in distributed problem solving and discuss their significance. We show that problem-solving networks have properties ~sparseness, small world, scaling regimes! that are like those displayed by information, biological, and technological networks. More importantly, we (...)
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  18. R. Brown, J. F. Glazebrook & I. C. Baianu (2007). A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems. [REVIEW] Axiomathes 17 (3-4):409-493.
    A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...)
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  19. Norbert Brunner (1983). The Axiom of Choice in Topology. Notre Dame Journal of Formal Logic 24 (3):305-317.
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  20. Gerd Buchdahl (1992). Science and God: The Topology of the Kantian World. Southern Journal of Philosophy 30 (S1):1-24.
    Kant maintains that in face of the failure of the traditional arguments for the existence of God it is necessary to provide an entirely fresh centre of gravity for the notion of religious consciousness. To explicate Kant's critique this paper develops, as a special hermeneutic device, the idea of a kind of Husserlian reduction and realization', in terms of which the various uses of Kant's concept of thing' or object' are given a new interpretation,using this to provide a novel approach (...)
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  21. Robert Warren Button (1978). A Note on the $Q$-Topology. Notre Dame Journal of Formal Logic 19 (4):679-686.
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  22. Craig Callendar & Robert Weingard (1996). An Introduction to Topology. The Monist 79 (1):21--33.
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  23. C. Callender & R. Weingard (2000). Topology Change and the Unity of Space. Studies in History and Philosophy of Science Part B 31 (2):227-246.
    Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general relativity (modulo (...)
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  24. Roberto Casati (2009). Does Topological Perception Rest on a Misconception About Topology? Philosophical Psychology 22 (1):77 – 81.
    In this article I assess some results that purport to show the existence of a type of 'topological perception', i.e., perceptually based classification of topological features. Striking findings about perception in insects appear to imply that (1) configural, global properties can be considered as primitive perceptual features, and (2) topological features in particular are interesting as they are amenable to formal treatment. I discuss four interrelated questions that bear on any interpretation of findings about the perception of topological properties: what (...)
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  25. Roberto Casati & Achille C. Varzi (2000). Topological Essentialism. Philosophical Studies 100 (3):217-236.
    Considering topology as an extension of mereology, this paper analyses topological variants of mereological essentialism (the thesis that an object could not have different parts than the ones it has). In particular, we examine de dicto and de re versions of two theses: (i) that an object cannot change its external connections (e.g., adjacent objects cannot be separated), and (ii) that an object cannot change its topological genus (e.g., a doughnut cannot turn into a sphere). Stronger forms of structural essentialism, (...)
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  26. Roberto Casati & Achille C. Varzi (1999). Parts and Places. The Structures of Spatial Representation. The Mit Press.
    Thinking about space is thinking about spatial things. The table is on the carpet; hence the carpet is under the table. The vase is in the box; hence the box is not in the vase. But what does it mean for an object to be somewhere? How are objects tied to the space they occupy? This book is concerned with these and other fundamental issues in the philosophy of spatial representation. Our starting point is an analysis of the interplay between (...)
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  27. Anthony G. Cohn & Achille C. Varzi (2003). Mereotopological Connection. Journal of Philosophical Logic 32 (4):357-390.
    The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified - the strength of (...)
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  28. Marcelo E. Coniglio & Francisco Miraglia (2000). Non-Commutative Topology and Quantales. Studia Logica 65 (2):223-236.
    The relationship between q-spaces (c.f. [9]) and quantum spaces (c.f. [5]) is studied, proving that both models coincide in the case of Spec A, the spectrum of a non-commutative C*-algebra A. It is shown that a sober T 1 quantum space is a classical topological space. This difficulty is circumvented through a new definition of point in a quantale. With this new definition, it is proved that Lid A has enough points. A notion of orthogonality in quantum spaces is introduced, (...)
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  29. Thierry Coquand (1997). Minimal Invariant Spaces in Formal Topology. Journal of Symbolic Logic 62 (3):689-698.
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  30. Thierry Coquand, Erik Palmgren & Bas Spitters (2011). Metric Complements of Overt Closed Sets. Mathematical Logic Quarterly 57 (4):373-378.
    We show that the set of points of an overt closed subspace of a metric completion of a Bishop-locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop-compact. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  31. John Earman (1977). How to Talk About the Topology of Time. Noûs 11 (3):211-226.
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  32. Ilijas Farah (2002). Review: Stevo Todorcevic, Topics in Topology. [REVIEW] Bulletin of Symbolic Logic 8 (4):526-528.
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  33. Ingo Farin (2007). Heidegger's Topology: Being, Place, World. Journal of Phenomenological Psychology 38 (2):288-295.
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  34. Nikolaus Fogle (2011). The Spatial Logic of Social Struggle: A Bourdieuian Topology. Lexington Books.
    This is the first work to explicitly target Bourdieu's philosophy of space as a basic organizing force for his social theory. It draws together his work on both social space and physical space, and it applies the logic that binds them together to problems of architecture and urban development.
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  35. Peter Forrest (1996). From Ontology to Topology in the Theory of Regions. The Monist 79 (1):34--50.
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  36. James Franklin (2014). Global and Local. Mathematical Intelligencer 36 (4).
    The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, (...)
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  37. Philip Franklin (1935). What is Topology? Philosophy of Science 2 (1):39-47.
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  38. Wolfgang Freitag (2009). Form and Philosophy: A Topology of Possibility and Representation. Synchron.
    Possibility and reference have been central topics in metaphysics and the philosophy of language in the past decades. Wolfgang Freitag’s Form and Philosophy provides a novel approach to these notions and their interrelations, based on the concept of form as the key modal concept: form is the possibility space of objects. In its historic dimension, the book analyses the role of form in Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and Immanuel Kant’s Critique of Pure Reason. In its systematic dimension, the book offers (...)
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  39. Stefan Geschke (2002). Applications of Elementary Submodels in General Topology. Synthese 133 (1-2):31 - 41.
    Elementary submodels of some initial segment of the set-theoretic universe are useful in order to prove certain theorems in general topology as well as in algebra. As an illustration we give proofs of two theorems due to Arkhangelskii concerning cardinal invariants of compact spaces.
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  40. Clark Glymour (1972). Topology, Cosmology and Convention. Synthese 24 (1-2):195 - 218.
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  41. E. R. Grosholz (1985). Two Episodes in the Unification of Logic and Topology. British Journal for the Philosophy of Science 36 (2):147-157.
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  42. W. Guz (1984). Stochastic Phase Spaces, Fuzzy Sets, and Statistical Metric Spaces. Foundations of Physics 14 (9):821-848.
    This paper is devoted to the study of the notion of the phase-space representation of quantum theory in both the nonrelativisitic and the relativisitic cases. Then, as a derived concept, the stochastic phase space is introduced and its connections with fuzzy set theory and probabilistic topological (in particular, metric) spaces are discussed.
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  43. Marion Haemmerli & Achille C. Varzi (2014). Adding Convexity to Mereotopology. In Pawel Garbacz & Oliver Kutz (eds.), Formal Ontology in Information Systems. Proceedings of the Eighth International Conference. IOS Press. 65–78.
    Convexity predicates and the convex hull operator continue to play an important role in theories of spatial representation and reasoning, yet their first-order axiomatization is still a matter of controversy. In this paper, we present a new approach to adding convexity to mereotopological theory with boundary elements by specifying first-order axioms for a binary segment operator s. We show that our axioms yields a convex hull operator h that supports, not only the basic properties of convex regions, but also complex (...)
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  44. James Harrington, Instants and Instantaneous Velocity.
    This paper will argue that the puzzles about instantaneous velocity, and rates of change more generally, are the result of a failure to recognize an ambiguity in the concept of an instant, and therefore of an instantaneous state. We will conclude that there are two distinct conceptions of a temporal instant: (i) instants conceived as fundamentally distinct zero-duration temporal atoms and (ii) instants conceived as the boundary of, or between,temporally extended durations. Since the concept of classical instantaneous velocity is well- (...)
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  45. Masoud Haveshki, Esfandiar Eslami & Arsham Borumand Saeid (2007). A Topology Induced by Uniformity on BL-Algebras. Mathematical Logic Quarterly 53 (2):162-169.
    In this paper, we consider a collection of filters of a BL-algebra A. We use the concept of congruence relation with respect to filters to construct a uniformity which induces a topology on A. We study the properties of this topology regarding different filters. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).
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  46. A. P. Hazen (1990). The Mathematical Philosophy of Contact. Philosophy 65 (252):205 - 211.
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  47. Adrian Heathcote (1988). Zeeman-Göbel Topologies. British Journal for the Philosophy of Science 39 (2):247-261.
    Zeeman argued that the Euclidean (i. e. manifold) topology of Minkowski space-time should be replaced by a strictly finer topology that was to have a closer connection with the indefinite metric. This proposal was extended in 1976 by Rudiger Göbel and Hawking, King and McCarthy to the space-times of General Relativity. It is the purpose of this paper to argue that these suggestions for replacement misrepresent the significance of the manifold topology and overstate the necessity for a finer topology. The (...)
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  48. Bernhard Heinemann (2008). A Hybrid Logic for Reasoning About Knowledge and Topology. Journal of Logic, Language and Information 17 (1):19-41.
    We extend Moss and Parikh’s bi-modal system for knowledge and effort by means of hybrid logic. In this way, some additional concepts from topology related to knowledge can be captured. We prove the soundness and completeness as well as the decidability of the extended system. Special emphasis will be placed on algebras.
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  49. Chris Heunen, Klaas Landsman & Bas Spitters, The Principle of General Tovariance.
    We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining (...)
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  50. H. M. Hubey (1997). Logic, Physics, Physiology, and Topology of Color. Behavioral and Brain Sciences 20 (2):191-194.
    This commentary starts with a simplified Cartesian vector space of the tristimulus theory of color. This vector space is then further simplified so that bitstrings are used to represent the vector space. The Commission Internationale de l'Eclairage (CIE) diagram is shown to follow directly and simply from this vector space. The Berlin & Kay results are shown to agree quite well with the vector space and the two-dimensional version of it, especially if the dimensions are normalized to take into account (...)
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