Theory of Topological Structures
Springer (Verlag)
978-94-010-7786-6 (ISBN)
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.
Reihe/Serie | Mathematics and Its Applications ; 39 | Mathematics and Its Applications ; 39 |
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Zusatzinfo | XII, 304 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 160 x 240 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
Mathematik / Informatik ► Mathematik ► Algebra | |
ISBN-10 | 94-010-7786-X / 940107786X |
ISBN-13 | 978-94-010-7786-6 / 9789401077866 |
Zustand | Neuware |
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