Introduction to Topology Notes

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1、Renzo’sMath490IntroductiontoTopologyTomBabinecChrisBestMichaelBlissNikolaiBrendlerEricFuAdrianeFungTylerKleinAlexLarsonTopcueLeeJohnMadonnaJoelMousseauNickPosavetzMattRosenbergDanielleRogersAndrewSardoneJustinShalerSmrithiSrinivasanPeteTroyanJacksonYimElizabethUibleDerekVanFarowePa

2、igeWarmkerZhengWuNinaZhangWinter2007Mathematics490–IntroductiontoTopologyWinter20072Contents1Topology91.1MetricSpaces......................................91.2OpenSets(inametricspace).............................101.3ClosedSets(inametricspace)............................111.4Topolo

3、gicalSpaces...................................111.5ClosedSets(Revisited).................................121.6Continuity........................................131.7Homeomorphisms....................................141.8HomeomorphismExamples..............................161.9Theore

4、msOnHomeomorphism............................181.10HomeomorphismsBetweenLettersofAlphabet...................191.10.1TopologicalInvariants.............................191.10.2Vertices.....................................191.10.3Holes......................................201.11Classi

5、ficationofLetters................................211.11.1Thecuriouscaseofthe“Q”..........................221.12TopologicalInvariants.................................231.12.1HausdorffProperty...............................231.12.2CompactnessProperty.............................241.12.

6、3ConnectednessandPathConnectednessProperties.............252MakingNewSpacesFromOld272.1CartesianProductsofSpaces.............................272.2TheProductTopology.................................282.3PropertiesofProductSpaces.............................293Mathematics490–Introduc

7、tiontoTopologyWinter20072.4IdentificationSpaces..................................302.5GroupActionsandQuotientSpaces.........................343FirstTopologicalInvariants373.1Introduction.......................................373.2Compactness......................................373.

8、2.1PreliminaryIdeas.......