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 continuously fascinating workout one has to head via sooner than you can actually learn nice works of literature within the unique language. the current e-book grew out of notes for an introductory topology direction on the college of Alberta. It presents a concise creation to set theoretic topology (and to a tiny bit of algebraic topology). it's obtainable to undergraduates from the second one yr on, yet even starting graduate scholars can make the most 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 heritage in calculus and trouble-free algebra, yet no longer unavoidably in actual or complicated research. In a few issues, the booklet 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 commonly, particularly for an intuitive facts of Tychonoff's theorem; a brief and stylish, yet little recognized facts for the Stone-Weierstrass theorem is given.

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