Author | Husain, Taqdir. author |
---|---|
Title | Topology and Maps [electronic resource] / by Taqdir Husain |
Imprint | Boston, MA : Springer US : Imprint: Springer, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-8798-9 |
Descript | XX, 337 p. online resource |
I. Preliminaries -- 1. Fundamental Notions of Set Theory -- 2. Relations and Mappings -- 3. Partial and Linear Orderings; Cartesian Products -- 4. Lattices -- 5. Algebraic Structures -- 6. Categories and Functors -- II. Topological Spaces -- 7. Open and Closed Sets -- 8. Topologies and Neighborhoods -- 9. Limit Points -- 10. Bases and Subbases -- 11. First and Second Countable Spaces -- 12. Metric Spaces -- 13. Nets -- 14. Filters -- 15. Topologies Defined by Other Topologies -- Examples and Exercises -- III. Continuity and Separation Axioms -- 16. Continuous and Open Mappings -- 17. Topologies Defined by Mappings -- 18. Separation Axioms -- 19. Continuous Functions on Normal Spaces -- Examples and Exercises -- IV. Methods for Constructing New Topological Spaces from Old -- 20. Subspaces -- 21. Topological Sums -- 22. Topological Products -- 23. Quotient Topology and Quotient Spaces -- 24. Projective and Inductive Limits -- Examples and Exercises -- V. Uniform Spaces -- 25. Uniformities and Topologies -- 26. Uniformity and Separation Axioms -- 27. Uniformizable Spaces -- 28. Uniform Continuity and Uniform Spaces -- 29. Completeness in Uniform Spaces -- 30. Completeness, Compactness, and Completions -- 31. Topological Groups and Topological Vector Spaces -- 32. Metrizability -- 33. Fixed Points -- 34. Proximity Spaces -- Examples and Exercises -- VI. Compact Spaces and Various Other Types of Spaces -- 35. Compact Spaces -- 36. Countable Compactness and Sequential Compactness -- 37. Compactness in Metric Spaces -- 38. Locally Compact Spaces -- 39. MB-Spaces -- 40. k-Spaces and kr-Spaces -- 41. Baire Spaces -- 42. Pseudocompact Spaces -- 43. Paracompact Spaces -- 44. Compactifications -- Examples and Exercises -- VII. Generalizations of Continuous Maps -- 45. Almost Continuous Maps -- 46. Closed Graphs -- 47. Almost Continuity and Closed Graphs -- 48. Graphically Continuous Maps -- 49. Nearly Continuous and w-Continuous Maps -- 50. Semicontinuous Maps -- 51. Approximately Continuous Functions -- 52. Applications of Almost Continuity -- Examples and Exercises -- VIE. Function Spaces -- 53. The Set of All Maps -- 54. Compact-Open Topology and the Topology of Joint Continuity -- 55. Subsets of FE with Induced Topologies -- 56. The Uniformities on FE -- 57.