topology 2ed - james munkres

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1、ContentsPreface......................................vii.....ANotetotheReader................................xiPartIGENERALTOPOLOGYChapter1SetTheoryandLogic.......................31FundamentalConcepts..........................42Functions.................................15L,.+3Relations......

2、...........................214TheIntegersandtheRealNumbers...................305CartesianProducts............................366Finitesets................................397CountableandUncountableSets....................44*8ThePrincipleofRecursiveDefinition..................52hF9InfiniteSets

3、andtheAxiomofChoice..................5710Well-orderedSets............................62*11TheMaximumPrinciple.........................68*SupplementaryExercises:Well-Ordering...................72ivContentsChapter2TopologicalSpacesandContinuousFunctions.........7512TopologicalSpaces...........

4、.................7513BasisforaTopology...........................7814TheOrderTopology...........................8415TheProductTopologyonXxY....................8616TheSubspaceTopology.........................8817ClosedSetsandLimitPoints......................9218ContinuousFunctions............

5、..............10219TheProductTopology..........................11220TheMetricTopology...........................11921TheMetricTopology(continued)....................129*22TheQuotientTopology.........................136*SupplementaryExercises:TopologicalGroups................145Chapter3Connec

6、tednessandCompactness.................14723ConnectedSpaces............................14824ConnectedSubspacesoftheRealLine.................153"25ComponentsandLocalConnectedness.................15926CompactSpaces.............................16327CompactSubspacesoftheRealLine..................

7、17228Limitpointcompactnes$........................17829LocalCompactness...........................182*SupplementaryExercises:Nets........................187Chapter4CountabilityandSeparationAxioms.......I30TheCountabilityAxioms......................