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E-raamat: Introduction to Topology

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  • Formaat: PDF+DRM
  • Sari: De Gruyter Textbook
  • Ilmumisaeg: 22-Feb-2016
  • Kirjastus: De Gruyter
  • Keel: eng
  • ISBN-13: 9783110378160
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Introduction to TopologySuurem pilt
  • Formaat: PDF+DRM
  • Sari: De Gruyter Textbook
  • Ilmumisaeg: 22-Feb-2016
  • Kirjastus: De Gruyter
  • Keel: eng
  • ISBN-13: 9783110378160
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The aim of the book is to give a broad introduction of topology to undergraduate students. It covers the most important and useful parts of the point-set as well as the combinatorial topology. The development of the material is from simple to complex, concrete to abstract, and appeals to the intuition of readers. Attention is also paid to how topology is actually used in the other fields of mathematics. Over 150 illustrations, 160 examples and 600 exercises will help readers to practice and fully understand the subject.



Contents: Set and Map Metric Space Graph Topology Topological Concepts Complex Topological Properties Surface Topics in Point Set Topology Index
1 Set and Map
1(24)
1.1 Set
1(5)
1.2 Map
6(7)
1.3 Counting
13(5)
1.4 Equivalence Relation and Quotient
18(7)
2 Metric Space
25(24)
2.1 Metric
25(5)
2.2 Ball
30(2)
2.3 Open Subset
32(6)
2.4 Continuity
38(5)
2.5 Limit Point
43(2)
2.6 Closed Subset
45(4)
3 Graph
49(14)
3.1 Seven Bridges in Konigsberg
49(3)
3.2 Proof of One-Trip Criterion
52(4)
3.3 Euler's Formula
56(3)
3.4 Application of Euler's Formula
59(4)
4 Topology
63(28)
4.1 Topological Basis and Subbasis
63(4)
4.2 Open Subset
67(3)
4.3 Topological Space
70(5)
4.4 Comparing Topologies
75(5)
4.5 Limit Point and Closed Subset
80(5)
4.6 Closure
85(6)
5 Topological Concepts
91(26)
5.1 Continuity
91(5)
5.2 Homeomorphism
96(5)
5.3 Subspace
101(4)
5.4 Product
105(4)
5.5 Quotient
109(8)
6 Complex
117(14)
6.1 Simplicial Complex
117(5)
6.2 CW-Complex
122(2)
6.3 Projective Space
124(3)
6.4 Euler Number
127(4)
7 Topological Properties
131(34)
7.1 Hausdorff Space
131(4)
7.2 Connected Space
135(4)
7.3 Path Connected Space
139(6)
7.4 Connected Component
145(2)
7.5 Compact Space
147(12)
7.6 Limit Point Compact Space
159(6)
8 Surface
165(24)
8.1 Manifold
165(2)
8.2 Surface
167(5)
8.3 Simplicial Surface
172(2)
8.4 Planar Diagram
174(3)
8.5 Cut and Paste
177(2)
8.6 Classification of Surface
179(3)
8.7 Recognition of Surface
182(7)
9 Topics in Point Set Topology
189(44)
9.1 Normal Space
189(4)
9.2 Paracompact Space
193(4)
9.3 Complete Metric Space
197(5)
9.4 Baire Category Theorem
202(8)
9.5 Infinite Product
210(7)
9.6 Space-Filling Curve
217(4)
9.7 Space of Maps
221(12)
Index 233
Min Yan, HongKong University of Science and Technology, HongKong.
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