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Topological Analysis [Hardback]

  • Formāts: Hardback, 138 pages, height x width: 235x152 mm, weight: 369 g
  • Sērija : Princeton Legacy Library
  • Izdošanas datums: 19-Apr-2016
  • Izdevniecība: Princeton University Press
  • ISBN-10: 0691651418
  • ISBN-13: 9780691651415
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Topological AnalysisPalielināt
  • Formāts: Hardback, 138 pages, height x width: 235x152 mm, weight: 369 g
  • Sērija : Princeton Legacy Library
  • Izdošanas datums: 19-Apr-2016
  • Izdevniecība: Princeton University Press
  • ISBN-10: 0691651418
  • ISBN-13: 9780691651415
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780691651415.html

Topological analysis consists of those basic theorems of analysis which are essentially topological in character, developed and proved entirely by topological and pseudotopological methods. The objective of this volume is the promotion, encouragement, and stimulation of the interaction between topology and analysis-to the benefit of both.


Originally published in 1964.


The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.


Preface to the Second Edition v
Preface to the First Edition vi
Introduction vii
Chapter I Introductory Topology
1 Operations with sets
3(1)
2 Metric spaces
3(1)
3 Open and closed sets. Limit points
4(1)
4 Separability. Countable basis
5(1)
5 Compact sets
5(1)
6 Diameters and distances
6(1)
7 Superior and inferior limits. Convergence
7(2)
8 Connected sets. Well-chained sets
9(2)
9 Limit theorem. Applications
11(1)
10 Continua
12(2)
11 Irreducible continua. Reduction theorem
14(1)
12 Locally connected sets
15(1)
13 Property S. Uniformly locally connected sets
16(3)
14 Cartesian product spaces
19(1)
Chapter II Mappings
1 Continuity
20(2)
2 Complete spaces. Extension of transformations
22(2)
3 Mapping theorems
24(2)
4 Arc wise connectedness. Accessibility
26(2)
5 Simple closed curves
28(1)
Chapter III Plane Topology
1 Jordan curve theorem
29(3)
2 Phragmen-Brouwer theorem. Torhorst theorem
32(2)
3 Plane separation theorem. Applications
34(2)
4 Subdivisions
36(5)
Chapter IV Complex Numbers. Functions of a Complex Variable
1 The complex number system
41(8)
2 Functions of a complex variable. Limits. Continuity
49(2)
3 Derivatives
51(1)
4 Differentiability conditions. Cauchy-Biemann equations
52(1)
5 The exponential and related functions
53(3)
Chapter V Topological Index
1 Exponential representation. Indices
56(4)
2 Traversals of simple arcs and simple closed curves
60(4)
3 Index invariance
64(3)
4 Traversals of region boundaries and region subdivisions
67(1)
5 Homotopy Index invariance
68(4)
Chapter VI Differentiable Functions
1 Index near a non-zero of the derivative
72(1)
2 Measure of the image of the zeros of the derivative
72(1)
3 Index
73(2)
4 The differential quotient function
75(2)
5 The second derivative
77(1)
6 Higher derivatives. Order at a point
77(2)
7 Lightness and openness. Applications
79(1)
8 The Cauchy Inequality
80(3)
Chapter VII Degree. Zeros. Sequences
1 Local topological analysis. Degree
83(1)
2 Rouche's Theorem. Zeros and poles
84(2)
3 Termwise differentiability
86(1)
4 Hurwitz's Theorem
87(1)
5 The Ascoli and Vitali Theorems
87(4)
Chapter VIII Open Mappings. Local Analysis
1 General Theorems. Property-S and local connectedness
91(3)
2 Extension of openness
94(1)
3 Open mappings on manifolds
94(2)
4 Open mappings on simple cells and manifolds
96(3)
5 Local topological analysis
99(2)
6 Degree. Compact mappings
101(2)
Chapter IX Global Analysis
1 The Stoilow Theorem
103(1)
2 Orientability
104(4)
3 Characteristic equation for compact manifolds
108(3)
Appendix. Topological Background for the Maximum Principle
1 Exponential representation. Indices
111(1)
2 Traversals
112(2)
3 Zeros and non-zeros of the derivative
114(2)
4 Index for differentiable functions. Maximum Principle
116(3)
Bibliography 119(2)
Supplement to Bibliography 121(2)
Index 123