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1、ThispageintentionallyleftblankCAMBRIDGETRACTSINMATHEMATICSGeneralEditorsB.BOLLOBAS,W.FULTON,A.KATOK,F.KIRWAN,´P.SARNAK,B.SIMON,B.TOTARO186Dimensions,Embeddings,andAttractorsDimensions,Embeddings,andAttractorsJAMESC.ROBINSONUniversityofWarwickcambridgeuniversitypressCambridge,N
2、ewYork,Melbourne,Madrid,CapeTown,Singapore,SaoPaulo,Delhi,Dubai,Tokyo,MexicoCityCambridgeUniversityPressTheEdinburghBuilding,CambridgeCB28RU,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521
3、898058CJ.C.Robinson2011Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished2011PrintedintheUnitedKingdomattheUn
4、iversityPress,CambridgeAcataloguerecordforthispublicationisavailablefromtheBritishLibraryLibraryofCongressCataloginginPublicationdataRobinson,JamesC.(JamesCooper),1969Dimensions,Embeddings,andAttractors/JamesC.Robinson.p.cm.(CambridgeTractsinMathematics;186)Includesbibliograph
5、icalreferencesandindex.ISBN978-0-521-89805-8(hardback)1.Dimensiontheory(Topology)2.Attractors(Mathematics)3.Topologicalimbeddings.I.Title.II.Series.QA611.3.R632011515.39dc222010042726ISBN978-0-521-89805-8HardbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceorac
6、curacyofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.Tomyfamily:Tania,Joseph,&Kate.ContentsPrefacepagexiIntroduction1PARTI:FINITE-DIMENSIONALSETS1Lebesguecoveringdim
7、ension71.1Coveringdimension81.2ThecoveringdimensionofIn101.3Embeddingsetswithfinitecoveringdimension121.4Largeandsmallinductivedimensions17Exercises182HausdorffmeasureandHausdorffdimension202.1HausdorffmeasureandLebesguemeasure202.2Hausdorffdimension232.3TheHausdorffdimensionof
8、products252.4Hausdorffdimensionandcoveringdimension26Exercise
