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1、SpringerMonographsinMathematicsForfurthervolumes:www.springer.com/series/3733StephenLeonLipscombFractalsandUniversalSpacesinDimensionTheoryWith91Illustrationsand10Tables123StephenLeonLipscombEmeritusProfessorofMathematicsDepartmentofMathematicsUniversityofMaryWashingto
2、nFredericksburg,VA22401USAslipscomb@umw.eduISSN:1439-7382ISBN:978-0-387-85493-9e-ISBN:978-0-387-85494-6DOI10.1007/978-0-387-85494-6LibraryofCongressControlNumber:2008938816MathematicsSubjectClassification(2000):54xx,28A80,57xxcSpringerScience+BusinessMedia,LLC2009Allri
3、ghtsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnec-tionwithanyformof
4、informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasan
5、expressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperspringer.comDedicatedtomywifePatty,oursonsStephenandDarrin,andmymotherDemaAnn(Alkire),andthememoryofmyfatherDavidLeonLipscombBalsa-woodmodelofJconstructedbyGeneMiller.151Photogr
6、aphbyMarlinThomas;graphicaladjustmentsbyBulentAtalay.ContentsPrefacexiIntroductionxiiiChapter1.ConstructionofJA=Jα1§1Baire’sZero-DimensionalSpaces1§2Adjacent-EndpointRelation4§3JAandtheNaturalMapp5§4Comments6Chapter2.Self-SimilarityandJn+1forFiniten11§5Self-Similarityo
7、fJA11§6Approximationsforn+1=2,3,412§7Approximationsforn+1=513§8JasanAttractorωnofanIFS16n+1§9CanWe“View”Jn+1in3-Space?20§10Comments21Chapter3.No-CarryPropertyofωA23§11ThreeExamples23§12StarSpaces25§13TheStarSpaceinl2(A)26§14ProjectingN(A)ontoaCantor-StarSubspace27§15P
8、rojectingJAontoaStarSubspace27§16MappingJintol2(A)28A§17No-CarryCharacterizationofωA29§18Comments31Chapter4.Imbeddi
