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Dynamic Topology

G. T. Whyburn, Edwin Duda (Autoren)

Buch | Hardcover

166 Seiten

1979
Springer-Verlag New York Inc.
978-0-387-90358-3 (ISBN)

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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.

A.- Section I Sets and Operations with Sets.- Section II Spaces.- Section III Directed Families.- Section IV Compact Sets and Bolzano-Weierstrass Sets.- Section V Functions.- Section VI Metric Spaces and a Metrization Theorem.- Section VII Diameters and Distances.- Section VIII Topological Limits.- Section IX Relativization.- Section X Connected Sets.- Section XI Connectedness of Limit Sets and Separations.- Section XII Continua.- Section XIII Irreducible Continua and a Reduction Theorem.- Section XIV Locally Connected Sets.- Section XV Property S and Uniformly Locally Connected Sets.- Section XVI Functions and Mappings.- Section XVII Complete Spaces.- First Semester Examination.- Section XVIII Mapping Theorems.- Section XIX Simple Arcs and Simple Closed Curves.- Section XX Arcwise Connectedness.- Appendix I Localization of Property S.- Appendix II Cyclic Element Theory.- B.- Section I Product Spaces.- Section II Decomposition Spaces.- Section III Component Decomposition.- Section IV Homotopy.- Section V Unicoherence.- Section VI Plane Topology.- Appendix Dynamic Topology.

Reihe/Serie	Undergraduate Texts in Mathematics
Zusatzinfo	biography
Verlagsort	New York, NY
Sprache	englisch
Gewicht	470 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-387-90358-5 / 0387903585
ISBN-13	978-0-387-90358-3 / 9780387903583
Zustand	Neuware