---

＜電子ブック＞
A Taste of Topology / by Volker Runde
(Universitext. ISSN:21916675)

版	1st ed. 2005.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	X, 177 p : online resource
著者標目	*Runde, Volker author SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Algebraic topology FREE:Topology FREE:Algebraic Topology
一般注記	Preface -- Introduction -- Set Theory -- Metric Spaces -- Set Theoretic Topology -- Systems of Continuous Functions -- Basic Algebraic Topology -- The Classical Mittag-Leffler Theorem Derived from Bourbaki’s -- Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces -- The Arzela-Ascoli Theorem -- References -- List of Symbols -- Index If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language. The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set-theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students can benefit from some parts. Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In some points, the book treats its material differently than other texts on the subject: * Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; * Nets are used extensively, in particular for an intuitive proof of Tychonoff's theorem; * A short and elegant, but little known proof for the Stone-Weierstrass theorem is given HTTP:URL=https://doi.org/10.1007/0-387-28387-0

 類似資料