topology(yan)

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1、TopologyMinYanMay17,2002Contents1SetandMap31.1SetandElement...................................31.2SetOperations....................................41.3Maps..........................................71.4EquivalenceRelation,Partition,andQuotient...................122MetricSpace182.1Metric......

2、...................................182.2Ball..........................................222.3OpenSubset......................................232.4Continuity.......................................292.5LimitPoint......................................332.6ClosedSubset.............................

3、........353GraphandNetwork383.1SevenBridgesinK¨onigsberg.............................383.2ProofofOne-TripCriteria..............................413.3EulerFormula.....................................433.4EmbeddingGraphs..................................453.5PlatonicSolids......................

4、..............474Topology494.1TopologicalBasisandSubbasis...........................494.2OpenSubset......................................524.3ComparingTopologies................................574.4ClosedSubsetandLimitPoint............................604.5Closure.............................

5、............6415BasicTopologicalConcepts685.1Continuity.......................................685.2Homeomorphism...................................725.3Subspace........................................755.4Product........................................785.5Quotient...........................

6、.............826Complex886.1SimplicialComplex..................................886.2CW-Complex.....................................926.3ProjectiveSpaces...................................946.4EulerNumber.....................................977Surface1007.1Manifold............................

7、............1007.2Surface.........................................1027.3SimplicialSurface...................................1067.4PlanarDiagramandCW-StructureofSurface...................1077.5CutandPaste.....................................1117.6Cl