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1、AnalysisonManifoldsJamesR.MunkresMassachusettsInstituteofTechnologyCambridge,MassachusettsoADDISON-WESLEYPUBLISHINGCOMPANYTheAdvancedBookProgramRedwoodCity,California?MenloPark,California?Reading,MassachusettsNewYork?DonMills,Ontado?Wokingham,UnitedKingdom?AmsterdamBonn?Sydney.Si
2、ngapore?Tokyo?Madrid.SanJuanPublisher:AllanM.WyldeProductionManager:JanV.BenesMarketingManager:LauraLikelyElectronicComposition:PeterVacekCoverDesign:IraFrankLibraryofCongressCataloging-in-PublicationDataMunkres,JamesR.,1930-Analysisonmanifolds/JamesR.Munkres.p.cm.Includesbibliog
3、raphicalreferences.1.Mathematicalanalysis.2.Manifolds(Mathematics)QA300.M751990516.3'6'20-dc2091-39786ISBN0-201-51035-9CIPThisbookwaspreparedusingtheTEXtypesettinglanguage.Copyright(±)1991byAddison-WesleyPublishingCompany,TheAdvancedBookProgram,350BridgeParkway,Suite209,RedwoodCi
4、ty,CA94065Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyform,orbyanymeans,elec-tronic,mechanical,photocopying,recordingorotherwise,withoutthepriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAmerica.Publishedsimu
5、ltaneouslyinCanada.ABCDEFGHIJ-MA-943210PrefaceThisbookisintendedasatextforacourseinanalysis,attheseniororfirst-yeargraduatelevel.Ayear-longcourseinrealanalysisisanessentialpartofthepreparationofanypotentialmathematician.Forthefirsthalfofsuchacourse,thereissubstantialagreementasto
6、whatthesyllabusshouldbe.Standardtopicsinclude:sequenceandseries,thetopologyofmetricspaces,andthederivativeandtheRiemannianintegralforfunctionsofasinglevariable.Thereareanumberofexcellenttextsforsuchacourse,includingbooksbyApostol[A],Rudin[Ru],Goldberg[Go],andRoyden[Ro],amongother
7、s.Thereisnosuchuniversalagreementastowhatthesyllabusofthesecondhalfofsuchacourseshouldbe.Partoftheproblemisthattherearesimplytoomanytopicsthatbelonginsuchacourseforonetobeabletotreatthemallwithintheconfinesofasinglesemester,atmorethanasuperficiallevel.AtM.I.T.,wehavedealtwiththep
8、roblembyofferingtwoindependentsecond-ter
