基础拓扑和几何讲义

图书标准信息

• 作者 [美]辛格 著
• 出版社 世界图书出版公司
• 出版时间 2009-03
• 版次 1
• ISBN 9787506292818
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 232页
• 正文语种 英语
• 原版书名 Lecture Notes on Elementary Topology and Geometry

【内容简介】

Atthepresenttime，theaverageundergraduatemathematicsmajorfindsmathematicsheavilycompartmentalized.Afterthecalculus，hetakesacourseinanalysisandacourseinalgebra.Dependinguponhisinterests（orthoseofhisdepartment），hetakescoursesinspecialtopics.Ifheisexposedtotopology，itisusuallystraightforwardpointsettopology;ifheisexposedtogeometry，itisusuallyclassicaldifferentialgeometry.

【目录】

ChapterSomepointsettopology
1.1Naivesettheory
1.2Topologicalspaces
1.3Connectedandcompactspaces
1.4Continuousfunctions
1.5Productspaces
1.6TheTychonofftheorem
Chapter2Morepointsettopology
2.1Separationaxioms
2.2Separationbycontinuousfunctions
2.3Moreseparability
2.4Completemetricspaces
2.5Applications
Chapter3Fundamentalgroupandcoveringspaces
3.1Homotopy
3.2Fundamentalgroup
3.3Coveringspaces
Chapter4Simplicialcomplexes
4.1Geometryofsimplicialcomplexes
4.2Baryccntricsubdivisions
4.3Simplicialapproximationtheorem
4.4Fundamentalgroupofasimplicialcomplex
Chapter5Manifolds
5.1Differentiablemanifolds
5.2Differentialforms
5.3Miscellaneousfacts
Chapter6HomologytheoryandtheDeRhamtheory
6.1Simplicialhomology
6.2DoRhamstheorem
Chapter7IntrinsicRiemanniangeometryofsurfaces
7.1Paralleltranslationandconnections
7.2Structuralequationsandcurvature
7.3Interpretationofcurvature
7.4Geodesiccoordinatesystems
7.5Isometricsandspacesofconstantcurvature
Chapter8ImbeddedmanifoldsinRa
Bibliography
Index