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拓扑学 英文版【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

拓扑学 英文版
  • （德）亚尼齐（JanichK.）著 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7510040647
  • 出版时间：2012
  • 标注页数：193页
  • 文件大小：31MB
  • 文件页数：204页
  • 主题词：拓扑－高等学校－教材－英文

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图书目录

Introduction1

1．What is point-set topology about?1

2．Origin and beginnings2

CHAPTER Ⅰ Fundamental Concepts5

1．Theconcept of a topological space5

2．Metric spaces7

3．Subspaces,disjoint unions and products9

4．Bases and subbases12

5．Continuous maps12

6．Connectedness14

7．The Hausdorff separation axiom17

8．Compactness18

CHAPTER Ⅱ Topological Vector Spaces24

1．The notion of a topological vector space24

2．Finite-dimensional vector spaces25

3．Hilbert spaces26

4．Banach spaces26

5．Fréchet spaces27

6．Locally convex topological vector spaces28

7．A couple of examples29

CHAPTER Ⅲ The Quotient Topology31

1．The notion of a quotient space31

2．Quotients and maps32

3．Properties of quotient spaces33

4．Examples:Homogeneous spaces34

5．Examples:Orbit spaces37

6．Examples:Collapsing a subspace to a point39

7．Examples:Gluing topological spaces together43

CHAPTER Ⅳ Completion of Metric Spaces50

1．The completion of a metric space50

2．Completion of a map54

3．Completion of normed spaces55

CHAPTER Ⅴ Homotopy59

1．Homotopic maps59

2．Homotopy equivalence61

3．Examples63

4．Categories66

5．Functors69

6．What is algebraic topology?70

7．Homotopy-what for?74

CHAPTER Ⅵ The Two Countability Axioms78

1．First and second countability axioms78

2．Infinite products80

3．The role of the countability axioms81

CHAPTER Ⅶ CW-Complexes87

1．Simplicial complexes87

2．Cell decompositions93

3．The notion of a CW-complex95

4．Subcomplexes98

5．Cell attaching99

6．Why CW-complexes are more flexible100

7．Yes,but...?102

CHAPTER Ⅷ Construction of Continuous Functions on Topological Spaces106

1．The Urysohn lemma106

2．The proof of the Urysohn lemma111

3．The Tietze extension lemma114

4．Partitions of unity and vector bundle sections116

5．Paracompactness123

CHAPTER Ⅸ Covering Spaces127

1．Topological spaces over Ⅹ127

2．The concept of a covering space130

3．Path lifting133

4．Introduction to the classification of covering spaces137

5．Fundamental group and lifting behavior141

6．The classification of covering spaces144

7．Covering transformations and universal cover149

8．The role of covering spaces in mathematics156

CHAPTER Ⅹ The Theorem of Tychonoff160

1．An unlikely theorem?160

2．What is it good for?162

3．The proof167

LAST CHAPTER Set Theory(by Theodor Br？cker）171

References177

Table of Symbols179

Index183

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