Download e-book for kindle: A Taste of Topology (Universitext) by Volker Runde

By Volker Runde

If arithmetic is a language, then taking a topology direction on the undergraduate point is cramming vocabulary and memorizing abnormal verbs: an important, yet now not consistently interesting workout one has to move via sooner than you can learn nice works of literature within the unique language. the current booklet grew out of notes for an introductory topology direction on the college of Alberta. It presents a concise advent to set theoretic topology (and to a tiny bit of algebraic topology). it truly is available to undergraduates from the second one 12 months on, yet even starting graduate scholars can reap the benefits of a few components. nice care has been dedicated to the choice of examples that aren't self-serving, yet already available for college kids who've a historical past in calculus and basic algebra, yet now not inevitably in actual or advanced research. In a few issues, the e-book treats its fabric in a different way than different texts at the topic: Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; nets are used broadly, specifically for an intuitive facts of Tychonoff's theorem; a quick and stylish, yet little recognized evidence for the Stone-Weierstrass theorem is given.

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