Read e-book online A Taste of Topology (Universitext) PDF

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 no longer regularly fascinating workout one has to move via prior to you could learn nice works of literature within the unique language. the current booklet grew out of notes for an introductory topology path on the college of Alberta. It presents a concise advent to set theoretic topology (and to a tiny bit of algebraic topology). it's available to undergraduates from the second one yr on, yet even starting graduate scholars can take advantage of a few elements. nice care has been dedicated to the choice of examples that aren't self-serving, yet already available for college kids who've a history in calculus and undemanding algebra, yet now not inevitably in actual or complicated research. In a few issues, the ebook 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, particularly for an intuitive evidence of Tychonoff's theorem; a quick and stylish, yet little recognized evidence for the Stone-Weierstrass theorem is given.

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A Taste of Topology (Universitext) by Volker Runde

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