Springer.Runde.V.A.taste.of.topology.(Universitext.Springer.2005)(ISBN.038725790X)(182s)

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1、UniversitextEditorialBoard(NorthAmerica):S.AxlerK.A.RibetVolkerRundeATasteofTopologyWith17FiguresVolkerRundeDepartmentofMathematicalandStatisticalSciencesUniversityofAlbertaEdmonton,AlbertaCanadaT6G2G1vrunde@ualberta.caEditorialBoard(NorthAmerica):K.

2、A.RibetS.AxlerMathematicsDepartmentMathematicsDepartmentUniversityofCaliforniaatBerkeleySanFranciscoStateUniversityBerkeley,CA94720-3840SanFrancisco,CA94132USAUSAribet@math.berkeley.eduaxler@sfsu.eduMathematicsSubjectClassification(2000):54-01,55-01L

3、ibraryofCongressControlNumber:2005924410ISBN-10:0-387-25790-XPrintedonacid-freepaper.ISBN-13:978-0387-25790-7©2005SpringerScience+BusinessMedia,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepub

4、lisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimil

5、arordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprie

6、taryrights.PrintedintheUnitedStatesofAmerica.(MVY)987654321springeronline.comVolkerRundeATasteofTopologyMarch14,2005SpringerBerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoPrefaceIfmathematicsisalanguage,thentakingatopologycourseattheundergradu-a

7、televeliscrammingvocabularyandmemorizingirregularverbs:anecessary,butnotalwaysexcitingexerciseonehastogothroughbeforeonecanreadgreatworksofliteratureintheoriginallanguage,whosebeautyeventually—inretrospect—compensatesforallthedrudgery.Set-theoreticto

8、pologyleavesitsmarkonmathematicsnotsomuchthroughpowerfultheorems(eventhoughtherearesome),butratherbypro-vidingaunifiedframeworkformanyphenomenainawiderangeofmathe-maticaldisciplines.Anintroductorycourseintopologyisnecessarilyconceptheavy;thenatureofth