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Topological Spaces
- 1st Edition - January 1, 1964
- Author: H. J. Kowalsky
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 5 2 4 - 7
Topological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary… Read more
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Request a sales quoteTopological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary principles, topological spaces, and compactness and connectedness. Discussions focus on locally compact spaces, local connectedness, fundamental concepts and their reformulations, lattice of topologies, axioms of separation, fundamental concepts of set theory, and ordered sets and lattices. The manuscript then ponders on mappings and extensions and characterization of topological spaces, including completely regular spaces, transference of topologies, Wallman compactification, and embeddings. The publication takes a look at metric and uniform spaces and applications of topological groups. Topics include the Stone-Weierstrass Approximation Theorem, extensions and completions of topological groups, topological rings and fields, extension and completion of uniform spaces, uniform continuity and uniform convergence, metric spaces, and metritization. The text is a valuable reference for mathematicians and researchers interested in the study of topological spaces.
PrefaceIntroductionI. Elementary Principles 1. Fundamental Concepts of Set Theory 2. Ordered Sets and Lattices 3. FiltersII. Topological Spaces 4. Topology and Limits 5. Fundamental Concepts and Their Reformulations 6. The Order Topology and Metric Spaces 7. The Lattice of Topologies 8. Axioms of Separation 9. Subspaces 10. Cardinality ConditionsIII. Compactness and Connectedness 11. Compactness 12. Locally Compact Spaces 13. Paracompact Spaces 14. Connectedness 15. Local ConnectednessIV. Mappings 16. Topological Maps, Homeomorphisms 17. Continuous Mappings 18. Completely Regular Spaces 19. Properties of Continuous Mappings 20. Transference of Topologies 21. Quotient Spaces 22. Product Spaces 23. Spaces of Mappings 24. Sums of SpacesV. Extensions and Characterization of Topological Spaces 25. Extensions of Topological Spaces 26. The Wallman Compactification 27. The Stone-Čech Compactification 28. Embeddings 29. Representation TheoremsVI. Metric and Uniform Spaces 30. Metric Spaces 31. Metrization 32. Extensions and Completions of Metric Spaces 33. Uniform Structures 34. Uniform Continuity and Uniform Convergence 35. Extension and Completion of Uniform SpacesVII. Topological Groups. Applications 36. Topological Groups 37. Extensions and Completions of Topological Groups 38. Topological Rings and Fields 39. Topological Vector Spaces. The Stone-Weierstrass Approximation Theorem 40. Inductive and Projective LimitsNotations EmployedBibliographySubject Index
- No. of pages: 296
- Language: English
- Edition: 1
- Published: January 1, 1964
- Imprint: Academic Press
- eBook ISBN: 9781483265247
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