Journal of Symbolic Logic 55 (2):589-603 (1990)
|Abstract||A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class. K is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y ∈ K and Y is equivalent to X, then Y is homeomorphic to X. As prime example, the closed set taxonomy assigns to each sentence in the first order language of bounded lattices the class of topological spaces whose lattices of closed sets satisfy that sentence. It turns out that every compact two-complex is characterized via this taxonomy in the class of metrizable spaces, but that no infinite discrete space is so characterized. We investigate various natural classification schemes, compare them, and look into the question of which spaces can and cannot be characterized within them|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Steffen Lewitzka (2007). Abstract Logics, Logic Maps, and Logic Homomorphisms. Logica Universalis 1 (2).
Andrzej W. Jankowski (1986). Some Modifications of Scott's Theorem on Injective Spaces. Studia Logica 45 (2):155 - 166.
Paul Bankston (1987). Reduced Coproducts of Compact Hausdorff Spaces. Journal of Symbolic Logic 52 (2):404-424.
Paul Bankston (1991). Corrigendum to "Taxonomies of Model-Theoretically Defined Topological Properties". Journal of Symbolic Logic 56 (2):425-426.
Katalin Bimbó (2007). Functorial Duality for Ortholattices and de Morgan Lattices. Logica Universalis 1 (2).
Bart Kuijpers, Jan Paredaens & Jan Van Den Bussche (2000). Topological Elementary Equivalence of Closed Semi-Algebraic Sets in the Real Plane. Journal of Symbolic Logic 65 (4):1530-1555.
Jörg Flum & Juan Carlos Martinez (1988). On Topological Spaces Equivalent to Ordinals. Journal of Symbolic Logic 53 (3):785-795.
Paul Bankston (1984). Expressive Power in First Order Topology. Journal of Symbolic Logic 49 (2):478-487.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Recent downloads (6 months)0
How can I increase my downloads?