Whyburn / Duda Dynamic Topology

Erscheinungsjahr 2012
ISBN: 978-1-4684-6262-3
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 154 Seiten, eBook

Reihe: Undergraduate Texts in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Whyburn, G.

Duda, E.

Inhaltsverzeichnis

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.