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General TopologyPDF|Epub|txt|kindle电子书版本网盘下载
- Waclaw Sierpinski 著
- 出版社：
- ISBN：
- 出版时间：1952
- 标注页数：290页
- 文件大小：71MB
- 文件页数：298页
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图书目录
Ⅰ．FRECHET (V)SPACES1
1．Fréchet (V)spaces3
2．Limit elements and derived sets3
3．Topological equivalence of (V)spaces4
4．Closed sets6
5．The closure of a set7
6．Open sets．The interior of a set11
7．Sets dense-in-themselves．The nucleus of a set．Scattered sets13
8．Sets closed in a given set15
9．Separated sets．Connected sets16
10．Images and inverse images of sets．Biuniform functions22
11．Continuity．Continuous images24
12．Conditions for continuity in a set26
13．A continuous image of a connected set27
14．Homeomorphic sets28
15．Topological properties31
16．Limit elements of order m．Elements of condensation．m-compact sets33
17．Cantor＇s theorem34
18．Topological limits of a sequence of sets36
Ⅱ．TOPOLOGICAL SPACES38
19．Topological spaces38
20．Properties of derived sets40
21．Properties of families of closed sets43
22．Properties of closure45
23．Examples of topological spaces47
24．Properties of relatively closed sets50
25．Homeomorphism in topological spaces50
26．The border of a set．Nowhere-dense sets52
Ⅲ．TOPOLOGICAL SPACES WITH A COUNTABLE BASIS58
27．Topological spaces with countable bases58
28．Hereditary separability of topological spaces with countable bases60
29．The power of an aggregate of open sets61
30．The countability of scattered sets62
31．The Cantor-Bendixson theorem63
32．The Lindelof and Borel-Lebesgue theorems65
33．Transfinite descending sequences of closed sets66
34．Bicompact sets69
Ⅳ．HAUSDORFF TOPOLOGICAL SPACES SATISFYING THE FIRST AXIOM OF COUNTABILITY72
35．Hausdorff topological spaces．The limit of a sequence．Fréchet＇s (L)class72
36．Properties of limit elements76
37．Properties of functions continuous in a given set78
38．The power of the aggregate of functions continuous in a given set．Topological types79
39．Continuous images of compact closed sets．Continua82
40．The inverse of a function continuous in a compact closed set85
41．The power of an aggregate of open (closed) sets88
Ⅴ．NORMAL TOPOLOGICAL SPACES90
42．Condition of normality90
43．The powers of a perfect compact set and a closed compact set92
44．Urysohn＇s lemma95
45．The power of a connected set97
Ⅵ．METRIC SPACES98
46．Metric spaces98
47．Congruence of sets．Equivalence by division100
48．Open spheres105
49．Continuity of the distance function106
50．Separable metric spaces107
51．Properties of compact sets109
52．The diameter of a set and its properties110
53．Properties equivalent to separability115
54．Properties equivalent to closedness and compactness117
55．The derived set of a compact set119
56．Condition for connectedness．ε-chains120
57．Hilbert space and its properties122
58．Urysohn＇s theorem．Dimensional types128
59．Fréchet＇s space Eω and its properties133
60．The 0-dimensional Baire space．The Cantor set142