Elements of the Theory of Functions and Functional Analysis vol1

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1、ELEMENTSOFTHETHEORYOFFUNCTIONSANDFUNCTIONALANALYSISVOLUME1METRICANDNORMEDSPACESOTHERGRAYLOCKPUBLICATIONSALEKSANDROV:CombinatorialTopologyVol.1:Introduction.Complexes.Coverings.DimensionVol.2:TheBettiGroupsVol.3:HomologicalManifolds.TheDualityTheorems.CohomologyGroupsofCompacta.ContinuousMap

2、PingsofPolyhedraKHlNCHIN:ThreePearlsofNumberTheoryMathematicalFoundationsofQuantumStatisticsKOLMOGOROVandFOMIN:ElementsoftheTheoryofFunctionsandFunctionalAnalysisVol.1:MetricandNormedSPacesVol.2:Measure.TheLebesgueIntegral.HilbertSpaceNOVOZHILOV:FoundationsoftheNonlinearTheoryofElasticityPE

3、TROVSKII:LecturesontheTheoryofIntegralEquationsPONTRYAGIN:FoundationsofCombinatorialTopologyElementsoftheTheoryofFunctionsandFunctionalAnalysisVOLUME1METRICANDNORMEDSPACESBYA.N.KOLMOGOROVANDS.V.FOMINrRANSLATEDFROMTHEFIRST(1954)RUSSIANEDITIONbyLEOF.BORONDepartmentofMathematicsUniversityofWis

4、consinGRAYLOCKPRESSROCHESTER,N.Y.1957Copyright,1957,byGRAYLOCKPRESSRochester,N.Y.Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyform,ortranslated,withoutpermis•sioninwritingfromthepublishers.LibraryofCongressCatalogCardNumber57-14021ThirdPrinting,July1963Ma....facturedi..l

5、AoU..iledStale.0/AmericaCONTENTSPreface.......................................................viiTranslator'sNote..............................................IXCHAPTERIFUNDAMENTALSOFSETTHEORY1.TheConceptofSet.OperationsonSets.......................12.FiniteandInfiniteSets.Denumerability...

6、...................33.EquivalenceofSets........................................6-I"TheNondenumerabilityoftheSetofRealNumbers............8.5.TheConceptofCardinalNumber............................96.PartitionintoClasses.......................................117.MappingsofSets.GeneralConceptof

7、Function................13CHAPTERIIMETRICSPACES8.DefinitionandExamplesofMetrioSpaces.....................169.ConvergenceofSequences.LimitPoints...........2310.OpenandClosedSets.......................................2611.OpenandClosedSetsontheRealLine....