Ebook: Dynamic Topology
- Tags: Topology
- Series: Undergraduate Texts in Mathematics
- Year: 1979
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
It is a privilege for me to write a foreword for this unusual book. The book is not primarily a reference work although many of the ideas and proofs are explained more clearly here than in any other source that I know. Nor is this a text of the customary sort. It is rather a record of a particular course and Gordon Whyburn's special method of teaching it. Perhaps the easiest way to describe the course and the method is to relate my own personal experience with a forerunner of this same course in the academic year 1937-1938. At that time, the course was offered every other year with a following course in algebraic topology on alternate years. There were five of us enrolled, and on the average we knew less mathematics than is now routinely given in a junior course in analysis. Whyburn's purpose, as we learned, was to prepare us in minimal time for research in the areas in which he was inter ested. His method was remarkable.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Sets and Operations with Sets....Pages 3-5
Spaces....Pages 6-11
Directed Families....Pages 12-13
Compact Sets and Bolzano-Weierstrass Sets....Pages 14-16
Functions....Pages 17-21
Metric Spaces and a Metrization Theorem....Pages 22-27
Diameters and Distances....Pages 28-30
Topological Limits....Pages 31-32
Relativization....Pages 33-33
Connected Sets....Pages 34-37
Connectedness of Limit Sets and Separations....Pages 38-40
Continua....Pages 41-42
Irreducible Continua and a Reduction Theorem....Pages 43-44
Locally Connected Sets....Pages 45-47
Property S and Uniformly Locally Connected Sets....Pages 48-50
Functions and Mappings....Pages 51-54
Complete Spaces....Pages 55-58
First Semester Examination....Pages 59-65
Mapping Theorems....Pages 66-69
Simple Arcs and Simple Closed Curves....Pages 70-73
Front Matter....Pages 1-1
Arcwise Connectedness....Pages 74-76
Front Matter....Pages 83-83
Product Spaces....Pages 85-92
Decomposition Spaces....Pages 93-99
Component Decomposition....Pages 100-104
Homotopy....Pages 105-110
Unicoherence....Pages 111-118
Plane Topology....Pages 119-129
Back Matter....Pages 145-154
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Sets and Operations with Sets....Pages 3-5
Spaces....Pages 6-11
Directed Families....Pages 12-13
Compact Sets and Bolzano-Weierstrass Sets....Pages 14-16
Functions....Pages 17-21
Metric Spaces and a Metrization Theorem....Pages 22-27
Diameters and Distances....Pages 28-30
Topological Limits....Pages 31-32
Relativization....Pages 33-33
Connected Sets....Pages 34-37
Connectedness of Limit Sets and Separations....Pages 38-40
Continua....Pages 41-42
Irreducible Continua and a Reduction Theorem....Pages 43-44
Locally Connected Sets....Pages 45-47
Property S and Uniformly Locally Connected Sets....Pages 48-50
Functions and Mappings....Pages 51-54
Complete Spaces....Pages 55-58
First Semester Examination....Pages 59-65
Mapping Theorems....Pages 66-69
Simple Arcs and Simple Closed Curves....Pages 70-73
Front Matter....Pages 1-1
Arcwise Connectedness....Pages 74-76
Front Matter....Pages 83-83
Product Spaces....Pages 85-92
Decomposition Spaces....Pages 93-99
Component Decomposition....Pages 100-104
Homotopy....Pages 105-110
Unicoherence....Pages 111-118
Plane Topology....Pages 119-129
Back Matter....Pages 145-154
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