Download A Taste of Topology (Universitext) by Volker Runde PDF

By Volker Runde

If arithmetic is a language, then taking a topology path on the undergraduate point is cramming vocabulary and memorizing abnormal verbs: an important, yet now not regularly fascinating workout one has to move via earlier than possible learn nice works of literature within the unique language. the current e-book grew out of notes for an introductory topology path on the collage of Alberta. It offers a concise creation to set theoretic topology (and to a tiny bit of algebraic topology). it truly is available to undergraduates from the second one yr on, yet even starting graduate scholars can make the most of a few elements. nice care has been dedicated to the choice of examples that aren't self-serving, yet already obtainable for college students who've a historical past in calculus and trouble-free algebra, yet now not unavoidably in actual or complicated research. In a few issues, the booklet treats its fabric otherwise than different texts at the topic: Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; nets are used widely, specifically for an intuitive evidence of Tychonoff's theorem; a quick and chic, yet little recognized evidence for the Stone-Weierstrass theorem is given.

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