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. & 120086;-Uniformities and & 120086;-Topologies. - 58. Equicontinuous Maps. - 59. Equicontinuity and Metric Spaces. - 60. Sequential Convergence in Function Spaces. - Examples and Exercises. - IX. Extensions of Mappings. - 61. Extensions of Maps on Completely Regular and Metric Spaces. - 62. The Hahn-Banach Extension Theorem. - 63. A General Extension Theorem. - Examples and Exercises. - X. C(X) Spaces. - 64. Stone-Weierstrass Theorem. - 65. Embeddings of X into C(X). - 66. C(X) Spaces for Compact Spaces X. - 67. Separability in C(X). - 68. C(X) Spaces for Completely Regular Spaces X. - 69. Characterization of Banach and Fréchet Spaces C(X). - 70. Characterization of Locally Convex Spaces C(X). - Epilogue. - Examples and Exercises. Language: English