General topology 一般拓扑学

Critically acclaimed text presents detailed theory of Fréchet (V) spaces and a comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. Numerous exercises reinforce teachings of each chapter. ". . . an elegant piece of work suitable for the beginning student and the mature mathematician."—Scripta Mathematica. 2nd edition.

Ⅰ.FRECHET SPACES
SECTION
　 1. Frechet (V)spaces
　 2. Limit elements and derived sets
　 3. Topological equivalence of (V)spaces
　 4. Closed sets
　 5. The closure of a set
　 6. Open sets. The interior of a set
　 7. Sets dense-in-themselves. The nucleus of a set. Scattered sets
　 8. Sets closed in a given set
　 9. Separated sets. Connected sets
10. Images and inverse images of sets. Biuniform functions
11. Continuity. Continuous images
12. Conditions for continuity in a set
13. A continuous image of a connected set
　 14. Homeomorphic sets
　 15. Topological properties
　 16. Limit elements of order m. Elements of condensation.m-compact sets
　 17. Cantor's theorem
　 18. Topological limits of a sequence of sets
Ⅱ. TOPOLOGICAL SPACES
　 19. Topological spaces
　20. Properties of derived sets
　21. Properties of families of closed sets
　22. Properties of closure
　23. Examples of topological spaces
　24. Properties of relatively closed sets
　 25. Homeomorphism in topological spaces
　26. The border of a set. Nowhere-dense sets
Ⅲ. TOPOLOGICAL SPACES WITH A COUNTABLE BASIS
　27. Topological spaces with countable bases
　28. Hereditary separability of topological spaces with countable
bases
29. The power of an aggregate of open sets
30. The countability of scattered sets
31. The Cantor-Bendixson theorem
32. The Lindel6f and Borel-Lebesgue theorems
33. Transfinite descending sequences of closed sets
34. Bicompact sets
Ⅳ. HAUSDORFF TOPOLOGICAL SPACES SATISFYING THE FI AXIOM OF COUNTABILITY
35. Hausdorff topological spaces. The limit of a sequence.Frechet's (L)class
36. Properties of limit elements
37. Properties of functions continuous in a given set
38. The power of the aggregate of functions continuous in a given set. Topological types
39. Continuous images of compact closed sets. Continua
40. The inverse of a function continuous in a compact closed set
41. The power of an aggregate of open (closed) sets
Ⅴ. NORMAL TOPOLOGICAL SPACES
42. Condition of normality
43. The powers of a perfect compact set and a closed compact set
44. Urysohn's lemma
45. The power of a connected set
Ⅵ. METRIC SPACES
46. Metric spaces
47. Congruence of sets. Equivalence by division
48. Open spheres
49. Continuity of the distance function
50. Separable metric spaces
51. Properties of compact sets
52. The diameter of a set and its properties
53. Properties equivalent to separability
54. Properties equivalent to closedness and compactness
55. The derived set of a compact set
56. Condition for connectedness. ,-chains
57. Hilbert space and its properties
58. Urysohn's theorem. Dimensional types
59. Fr6chet's space E~ and its properties
60. The 0-dimensional Baire space. The Cantor set
……
Ⅶ.COMPLETE SPACES
APPENDIX
NOTES
INDEX