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[德] 亚尼齐 著 / 世界图书出版公司 / 2012-01 / 平装
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拓扑学
Thisvolumecoversapproximatelytheamountofpoint-settopologythatastudentwhodoesnotintendtospecializeinthefieldshouldneverthelessknow.Thisisnotawholelot,andincondensedformwouldoccupyperhapsonlyasmallbooklet.Ouraim,however,wasnoteconomyofwords,butalivelypresentationoftheideasinvolved,anappealtointuitioninboththeimmediateandthehighermeanings.
作者:(德)亚尼齐
Introduction1.whatispoint-settopologyabout?2.originandbeginningsChapterⅠfundamentalconcepts1.theconceptofatopologicalspace2.metricspaces3.subspaces,disjointunionsandproducts4.rasesandsubbases5.continuousmaps6.connectedness7.thehausdorffseparationaxiom8.compactnessChapterⅡtopologicalvectorspaces1.thenotionofatopologicalvectorspace2.finite-dimensionalvectorspaces3.hilbertspaces4.banachspaces5.frechetspaces6.locallyconvextopologicalvectorspaces7.acoupleofexamplesChapterⅢthequotienttopology1.thenotionofaquotientspace2.quotientsandmaps3.propertiesofquotientspaces4.examples:homogeneousspaces5.examples:orbitspaces6.examples:collapsingasubspacetoapoint7.examples:gluingtopologicalspacestogetherChapterⅣcompletionofmetricspaces1.thecompletionofametricspace2.completionofamap3.completionofnormedspacesChapterⅤhomotopy1.homotopicmaps2.homotopyequivalence3.examples4.categories5.functors6.whatisalgebraictopology?7.homotopy--whatfor?ChapterⅥthetwocountabilityaxioms1.firstandsecondcountabilityaxioms2.infiniteproducts3.theroleofthecountabilityaxiomsChapterⅦcw-complexes1.simplicialcomplexes2.celldecompositions3.thenotionofacw-complex4.subcomplexes5.cellattaching6.whycw-complexesaremoreflexible7.yes,but...?ChapterⅧconstructionofcontinuousfunctionsontopologicalspaces1.theurysohnlemma2.theproofoftheurysohnlemma3.thetietzeextensionlemma4.partitionsofunityandvectorbundlesections5.paracompactnessChapterⅨcoveringspaces1.topologicalspacesoverx2.theconceptofacoveringspace3.pathlifting4.introductiontotheclassificationofcoveringspaces5.fundamentalgroupandliftingbehavior6.theclassificationofcoveringspaces7.coveringtransformationsanduniversalcover8.theroleofcoveringspacesinmathematicsChapterⅩthetheoremoftychonoff1.anunlikelytheorem?2.whatisitgoodfor?3.theprooflastChaptersettheory(bytheodorbr6cker)referencestableofsymbolsindex
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