topology 2ed - james munkres

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

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

3、...........52hF9InfiniteSetsandtheAxiomofChoice..................5710Well-orderedSets............................62*11TheMaximumPrinciple.........................68*SupplementaryExercises:Well-Ordering...................72ivContentsChapter2TopologicalSpacesandContinuousFunction

4、s.........7512TopologicalSpaces............................7513BasisforaTopology...........................7814TheOrderTopology...........................8415TheProductTopologyonXxY....................8616TheSubspaceTopology.........................8817ClosedSetsandLimitPoints.

5、.....................9218ContinuousFunctions..........................10219TheProductTopology..........................11220TheMetricTopology...........................11921TheMetricTopology(continued)....................129*22TheQuotientTopology.........................136*Sup

6、plementaryExercises:TopologicalGroups................145Chapter3ConnectednessandCompactness.................14723ConnectedSpaces............................14824ConnectedSubspacesoftheRealLine.................153"25ComponentsandLocalConnectedness.................15926CompactSpa

7、ces.............................16327CompactSubspacesoftheRealLine..................17228Limitpointcompactnes$........................17829LocalCompactness...........................182*SupplementaryExercises:Nets........................187Chapter4CountabilityandSeparationAxiom

8、s.......I30TheCountabilityAxioms......................