Elementary Topology Problem Book

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1、ElementaryTopologyProblemTextbookO.Ya.Viro,O.A.Ivanov,N.Yu.Netsvetaev,V.M.KharlamovDedicatedtothememoryofVladimirAbramovichRokhlin(1919–1984)–ourteacherContentsIntroductionxiPart1.GeneralTopologyChapterI.StructuresandSpaces31.Set-TheoreticDigression:Sets32.Topo

2、logyonaSet113.Bases164.MetricSpaces185.Subspaces276.PositionofaPointwithRespecttoaSet297.OrderedSets358.CyclicOrders42ChapterII.Continuity459.Set-TheoreticDigression:Maps4510.ContinuousMaps4911.Homeomorphisms57ChapterIII.TopologicalProperties6712.Connectedness6

3、713.ApplicationofConnectedness7314.PathConnectedness7615.SeparationAxioms81viiviiiContents16.CountabilityAxioms8717.Compactness9218.SequentialCompactness9819x.LocalCompactnessandParacompactness101ChapterIV.TopologicalConstructions10720.Multiplication10721.Quoti

4、entSpaces11322.ZooofQuotientSpaces11723.ProjectiveSpaces12724x.FiniteTopologicalSpaces13125x.SpacesofContinuousMaps135ChapterV.TopologicalAlgebra13926x.GeneralitiesonGroups14127x.TopologicalGroups14728x.Constructions15129x.ActionsofTopologicalGroups156Part2.Ele

5、mentsofAlgebraicTopologyChapterVI.FundamentalGroup16330.Homotopy16331.HomotopyPropertiesofPathMultiplication16832.FundamentalGroup17133.TheRoleofBasePoint176ChapterVII.CoveringSpacesandCalculationofFundamentalGroups17934.CoveringSpaces17935.TheoremsonPathLiftin

6、g18336.CalculationofFundamentalGroupsbyUsingUniversalCoverings185ChapterVIII.FundamentalGroupandMaps19137.InducedHomomorphismsandTheirFirstApplications19138.RetractionsandFixedPoints19739.HomotopyEquivalences20040.CoveringSpacesviaFundamentalGroups205Contentsix

7、41x.ClassificationofCoveringSpaces207ChapterIX.CellularTechniques21342.CellularSpaces21343x.TopologicalPropertiesofCellularSpaces22044.CellularConstructions22245.One-DimensionalCellularSpaces22546.FundamentalGroupofaCellularSpace229Bibliography239Index241Introdu

8、ctionThesubjectofthebook:ElementaryTopologyElementarymeansclosetoelements,basics.Itisimpossibletodeter-mineprecisely,onceandforall,whichtopologyiselementaryandwhichisnot.The