Theory of Topological Structures An Approach to Categorical Topology
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathe...
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| Format: | eBook |
| Language: | English |
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Dordrecht
Springer Netherlands
1988, 1988
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| Edition: | 1st ed. 1988 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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