000			02997nam a22004815i 4500
001			978-0-387-28387-6
003			DE-He213
005			20161121230926.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780387283876 _9978-0-387-28387-6
024	7		_a10.1007/0-387-28387-0 _2doi
050		4	_aQA611-614.97
072		7	_aPBP _2bicssc
072		7	_aMAT038000 _2bisacsh
082	0	4	_a514 _223
100	1		_aRunde, Volker. _eauthor.
245	1	2	_aA Taste of Topology _h[electronic resource] / _cby Volker Runde ; edited by S Axler, K.A. Ribet.
264		1	_aNew York, NY : _bSpringer New York, _c2005.
300			_aX, 182 p. 17 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aPreface -- 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.
520			_aIf 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.
650		0	_aMathematics.
650		0	_aTopology.
650		0	_aAlgebraic topology.
650	1	4	_aMathematics.
650	2	4	_aTopology.
650	2	4	_aAlgebraic Topology.
700	1		_aAxler, S. _eeditor.
700	1		_aRibet, K.A. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387257907
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-28387-0
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506008 _d506008