02990nam a22004695i 4500 978-0-387-28387-6 DE-He213 20260521091848.0 cr nn 008mamaa 100301s2005 xxu| s |||| 0|eng d 9780387283876 99780387283876 10.1007/0-387-28387-0 doi CICY 514 23 Runde, Volker. author. A Taste of Topology [recurso electrónico] / by Volker Runde ; edited by S Axler, K.A. Ribet. New York, NY : Springer New York, 2005. X, 176 p. 17 illus. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Universitext Preface -- Introduction -- Set Theory -- Metric Spaces -- Set Theoretic Topology -- Systems of Continuous Functions -- Basic Algebraic Topology -- The Classical Mittag-Leffler Theorem Derived from Bourbaki's -- Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces -- The Arzela-Ascoli Theorem -- References -- List of Symbols -- Index. 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 set-theoretic 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 self-serving, 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 Mittag-Leffler 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 Stone-Weierstrass theorem is given. MATHEMATICS. TOPOLOGY. ALGEBRAIC TOPOLOGY. MATHEMATICS. TOPOLOGY. ALGEBRAIC TOPOLOGY. Axler, S. editor. Ribet, K.A. editor. SpringerLink (Online service) Springer eBooks Printed edition: 9780387257907 Universitext http://dx.doi.org/10.1007/0-387-28387-0 Ver el texto completo en las instalaciones del CICY ddc ER 32754 32754 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 514 2025-07-10 08:39:41 2025-07-10 ER