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A Taste of Topologyby Volker Runde
Synopses & ReviewsPublisher Comments: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 settheoretic 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 selfserving, 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 MittagLeffler 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 StoneWeierstrass theorem is given.
Synopsis:Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to settheoretic topology. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective.
Synopsis:This should be a revelation for mathematics undergraduates. Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to settheoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The wellchosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective.
Table of ContentsPreface. Introduction. Set Theory. Metric Spaces. Set Theoretic Topology. Systems of Continuous Functions. Basic Algebraic Topology. The Classical MittagLeffler Theorem Derived from Bourbaki's. Failure of the HeineBorel Theorem in InfiniteDimensional Spaces. The ArzelaAscoli Theorem. References. List of Symbols. Index.
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