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
装帧平装
货号A3
上书时间2024-12-23
商品详情
- 品相描述:九品
图书标准信息
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作者
[德]亚尼齐 著
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出版社
世界图书出版公司
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出版时间
2012-01
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版次
1
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ISBN
9787510040641
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定价
29.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
192页
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正文语种
英语
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原版书名
Undergraduate Texts in mathematics:Klaus Jǎnich Topology
- 【内容简介】
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Thisvolumecoversapproximatelytheamountofpoint-settopologythatastudentwhodoesnotintendtospecializeinthefieldshouldneverthelessknow.Thisisnotawholelot,andincondensedformwouldoccupyperhapsonlyasmallbooklet.Ouraim,however,wasnoteconomyofwords,butalivelypresentationoftheideasinvolved,anappealtointuitioninboththeimmediateandthehighermeanings.
- 【作者简介】
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作者:(德)亚尼齐
- 【目录】
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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
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