topology 2ed - james munkres

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

2、.....................214TheIntegersandtheRealNumbers...................305CartesianProducts............................366Finitesets................................397CountableandUncountableSets....................44*8ThePrincipleofRecursiveDefinition..................52hF9InfiniteSetsandtheAxiomo

3、fChoice..................5710Well-orderedSets............................62*11TheMaximumPrinciple.........................68*SupplementaryExercises:Well-Ordering...................72ivContentsChapter2TopologicalSpacesandContinuousFunctions.........7512TopologicalSpaces............................7

4、513BasisforaTopology...........................7814TheOrderTopology...........................8415TheProductTopologyonXxY....................8616TheSubspaceTopology.........................8817ClosedSetsandLimitPoints......................9218ContinuousFunctions..........................10219ThePr

5、oductTopology..........................11220TheMetricTopology...........................11921TheMetricTopology(continued)....................129*22TheQuotientTopology.........................136*SupplementaryExercises:TopologicalGroups................145Chapter3ConnectednessandCompactness.........

6、........14723ConnectedSpaces............................14824ConnectedSubspacesoftheRealLine.................153"25ComponentsandLocalConnectedness.................15926CompactSpaces.............................16327CompactSubspacesoftheRealLine..................17228Limitpointcompactnes$..........

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