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[美] 辛格 著 / 世界图书出版公司 / 2009-03 / 平装
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基础拓扑和几何讲义
Atthepresenttime,theaverageundergraduatemathematicsmajorfindsmathematicsheavilycompartmentalized.Afterthecalculus,hetakesacourseinanalysisandacourseinalgebra.Dependinguponhisinterests(orthoseofhisdepartment),hetakescoursesinspecialtopics.Ifheisexposedtotopology,itisusuallystraightforwardpointsettopology;ifheisexposedtogeometry,itisusuallyclassicaldifferentialgeometry.
ChapterSomepointsettopology1.1Naivesettheory1.2Topologicalspaces1.3Connectedandcompactspaces1.4Continuousfunctions1.5Productspaces1.6TheTychonofftheoremChapter2Morepointsettopology2.1Separationaxioms2.2Separationbycontinuousfunctions2.3Moreseparability2.4Completemetricspaces2.5ApplicationsChapter3Fundamentalgroupandcoveringspaces3.1Homotopy3.2Fundamentalgroup3.3CoveringspacesChapter4Simplicialcomplexes4.1Geometryofsimplicialcomplexes4.2Baryccntricsubdivisions4.3Simplicialapproximationtheorem4.4FundamentalgroupofasimplicialcomplexChapter5Manifolds5.1Differentiablemanifolds5.2Differentialforms5.3MiscellaneousfactsChapter6HomologytheoryandtheDeRhamtheory6.1Simplicialhomology6.2DoRhamstheoremChapter7IntrinsicRiemanniangeometryofsurfaces7.1Paralleltranslationandconnections7.2Structuralequationsandcurvature7.3Interpretationofcurvature7.4Geodesiccoordinatesystems7.5IsometricsandspacesofconstantcurvatureChapter8ImbeddedmanifoldsinRaBibliographyIndex
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