Michael Henle A Combinatorial Introduction to Topology 1994英文文献资料

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1、ACombinatorialIntroductiontoTopologyMichaelHenleOberlinCollegeDOVERPUBLICATIONS,INC.NewYorkCopyrightCopyright©1979byMichaelHenle.AllrightsreservedunderPanAmericanandInternationalCopyrightConventions.BibliographicalNoteThisDoveredition,firstpublishedin1994,isanunabridgedandcorrectedrepub•lication

2、oftheworkfirstpublishedbyW.H.FreemanandCompany,SanFrancisco,in1979.LibraryofCongressCataloging-in-PublicationDataHenle,Michael.Acombinatorialintroductiontotopology/MichaelHenle.p.cm.Originallypublished:SanFrancisco:W.H.Freeman,1979.Includesbibliographicalreferencesandindex.ISBN0-486-67966-71.Alg

3、ebraictopology.I.Title.QA612.H461994514'.2—dc2093-50761CIPManufacturedintheUnitedStatesofAmericaDoverPublications,Inc.,31East2ndStreet,Mineola,N.Y.11501"Liberte,egalite,homologiesContentsChapterOneBasicConcepts§1TheCombinatorialMethod1§2ContinuousTransformationsinthePlane11§3CompactnessandConnec

4、tedness22§4AbstractPointSetTopology28ChapterTwoVectorFields§5ALinkBetweenAnalysisandTopology33ivCONTENTS§6Sperner'sLemmaandtheBrouwerFixedPointTheorem36§7PhasePortraitsandtheIndexLemma43§8WindingNumbers48§9IsolatedCriticalPoints54§10ThePoincareIndexTheorem60§11ClosedIntegralPaths67§12FurtherResu

5、ltsandApplications73ChapterThreePlaneHomologyandtheJordanCurveTheorem§13PolygonalChains79§14TheAlgebraofChainsonaGrating84§15TheBoundaryOperator88§16TheFundamentalLemma91§17Alexander'sLemma97§18ProofoftheJordanCurveTheorem100ChapterFourSurfaces§19ExamplesofSurfaces104§20TheCombinatorialDefinitio

6、nofaSurface116§21TheClassificationTheorem122§22SurfaceswithBoundary129CONTENTSVChapterFiveHomologyofComplexes§23Complexes132§24HomologyGroupsofaComplex143§25Invariance153§26BettiNumbersandtheEulerCharacteristic159§27MapColoringandRegularComplexes169§28GradientVectorFields176§29IntegralHomology18

7、5§30TorsionandOrientability192§31ThePoincareIndexTheoremAgain200ChapterSixContinuousTransformations§32CoveringSpaces209§33SimplicialTransformations221§34InvarianceAgain228§35Matrixes234§36TheLefschetzFixedPointTheorem242§37H