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- W653208557 abstract "0. Preliminaries.- 0.1 Conglomerates, classes and sets.- 0.2 Some categorical concepts.- 0.3 Uniform structures.- 1. Topological categories.- 1.1 Definitions and examples.- 1.2 Special categorical properties of topological categories.- 1.3 Relative connectednesses and disconnectednesses in topological categories.- 2. Reflective and coreflective subcategories.- 2.1 Universal maps and adjoint functors.- 2.2 Definitions and characterization theorems of E-reflective and M-coreflective subcategories.- 2.3 E-reflective and M-coreflective hulls.- 2.4 Reflectors as composition of epireflectors.- 3. Relations between special topological categories.- 3.1 The category Near and its subcategories.- 3.1.1 Topological spaces.- 3.1.2 Uniform spaces.- 3.1.3 Contigual spaces.- 3.2 The category P-Near and its subcategories.- 3.2.1 Prenearness spaces.- 3.2.2 Seminearness spaces.- 3.2.3 Grill-determined prenearness spaces.- 4. Cartesian closed topological categories.- 4.1 Definitions and equivalent characterizations.- 4.2 Examples.- 5. Topological functors.- 5.1 Factorization structures.- 5.2 Definitions and properties of topological functors.- 5.3 Initially structured categories.- 6. Completions.- 6.1 Initial and final completions.- 6.2 Completion of nearness spaces.- 7. Cohomology and dimension of nearness spaces.- 7.1 Cohomology theories for nearness spaces.- 7.2 Normality and dimension of nearness spaces.- 7.3 A cohomological characterization of dimension.- Appendix. Representable functors.- Exercises." @default.
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- W653208557 date "2011-11-03" @default.
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- W653208557 title "Theory of Topological Structures: An Approach to Categorical Topology" @default.
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