拓扑学

图书标准信息

• 作者 [德]亚尼齐 著
• 出版社 世界图书出版公司
• 出版时间 2012-01
• 版次 1
• ISBN 9787510040641
• 定价 29.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 192页
• 正文语种 英语
• 原版书名 Undergraduate Texts in mathematics:Klaus Jǎnich Topology

【内容简介】

Thisvolumecoversapproximatelytheamountofpoint-settopologythatastudentwhodoesnotintendtospecializeinthefieldshouldneverthelessknow.Thisisnotawholelot，andincondensedformwouldoccupyperhapsonlyasmallbooklet.Ouraim，however，wasnoteconomyofwords，butalivelypresentationoftheideasinvolved，anappealtointuitioninboththeimmediateandthehighermeanings.

【作者简介】

作者:(德)亚尼齐

【目录】

Introduction
1.whatispoint-settopologyabout?
2.originandbeginnings
ChapterⅠfundamentalconcepts
1.theconceptofatopologicalspace
2.metricspaces
3.subspaces,disjointunionsandproducts
4.rasesandsubbases
5.continuousmaps
6.connectedness
7.thehausdorffseparationaxiom
8.compactness

ChapterⅡtopologicalvectorspaces
1.thenotionofatopologicalvectorspace
2.finite-dimensionalvectorspaces
3.hilbertspaces
4.banachspaces
5.frechetspaces
6.locallyconvextopologicalvectorspaces
7.acoupleofexamples

ChapterⅢthequotienttopology
1.thenotionofaquotientspace
2.quotientsandmaps
3.propertiesofquotientspaces
4.examples:homogeneousspaces
5.examples:orbitspaces
6.examples:collapsingasubspacetoapoint
7.examples:gluingtopologicalspacestogether

ChapterⅣcompletionofmetricspaces
1.thecompletionofametricspace
2.completionofamap
3.completionofnormedspaces

ChapterⅤhomotopy
1.homotopicmaps
2.homotopyequivalence
3.examples
4.categories
5.functors
6.whatisalgebraictopology?
7.homotopy--whatfor?
ChapterⅥthetwocountabilityaxioms
1.firstandsecondcountabilityaxioms
2.infiniteproducts
3.theroleofthecountabilityaxioms
ChapterⅦcw-complexes
1.simplicialcomplexes
2.celldecompositions
3.thenotionofacw-complex
4.subcomplexes
5.cellattaching
6.whycw-complexesaremoreflexible
7.yes,but...?

ChapterⅧconstructionofcontinuousfunctionsontopologicalspaces
1.theurysohnlemma
2.theproofoftheurysohnlemma
3.thetietzeextensionlemma
4.partitionsofunityandvectorbundlesections
5.paracompactness

ChapterⅨcoveringspaces
1.topologicalspacesoverx
2.theconceptofacoveringspace
3.pathlifting
4.introductiontotheclassificationofcoveringspaces
5.fundamentalgroupandliftingbehavior
6.theclassificationofcoveringspaces
7.coveringtransformationsanduniversalcover
8.theroleofcoveringspacesinmathematics

ChapterⅩthetheoremoftychonoff
1.anunlikelytheorem?
2.whatisitgoodfor?
3.theproof
lastChapter
settheory（bytheodorbr6cker）
references
tableofsymbols
index