Author | Preuss, Gerhard. author |
---|---|
Title | Theory of Topological Structures [electronic resource] : An Approach to Categorical Topology / by Gerhard Preuss |
Imprint | Dordrecht : Springer Netherlands, 1988 |
Connect to | http://dx.doi.org/10.1007/978-94-009-2859-6 |
Descript | XII, 304 p. online resource |
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 -- 3.2 The category P-Near and its subcategories -- 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