拓扑学
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作者(德)亚尼齐
出版社世界图书出版公司
ISBN9787510040641
出版时间2012-08
版次1
装帧平装
开本16开
纸张胶版纸
页数192页
定价29元
上书时间2024-08-01
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基本信息
书名:拓扑学
定价：29.00元
作者:(德)亚尼齐
出版社：世界图书出版公司
出版日期：2012-08-01
ISBN：9787510040641
字数：
页码：192
版次：1
装帧：平装
开本：12开
商品重量：
编辑推荐
《拓扑学(英文版)》由世界图书出版公司北京公司出版。
内容提要
亚尼齐编著的《拓扑学》内容介绍：This volume covers appromately the amount ofpoint-set topology that a student who does not intend to specializein the field should nevertheless know.This is not a whole lot, andin condensed form would occupy perhaps only a small booklet. Ouraim, however, was not economy of words, but a lively presentationof the ideas involved, an appeal to intuition in both the immediateand the higher meanings.
目录
Introductio 1.what is point-set topology about? 2.origin and beginningsChapter Ⅰ fundamental concepts 1.the concept of a topological space 2.metric spaces 3.subspaces, disjoint unions and products 4.rases and subbases 5.continuous maps 6.connectedness 7.the hausdorff separation aom 8.compactnessChapter Ⅱ topological vector spaces 1.the notion of a topological vector space 2.finite-dimensional vector spaces 3.hilbert spaces 4.banach spaces 5.frechet spaces 6.locally convex topological vector spaces 7.a couple of examplesChapter Ⅲ the quotient topology 1.the notion of a quotient space 2.quotients and maps 3.properties of quotient spaces 4.examples: homogeneous spaces 5.examples: orbit spaces 6.examples: collapsing a subspace to a point 7.examples: gluing topological spaces togetherChapter Ⅳ completion of metric spaces 1.the completion of a metric space 2.completion of a map 3.completion of normed spacesChapter Ⅴ homotopy 1.homotopic maps 2.homotopy equivalence 3.examples 4.categories 5.functors 6.what is algebraic topology? 7.homotopy--what for?Chapter Ⅵ the two countability aoms 1.first and second countability aoms 2.infinite products 3.the role of the countability aomsChapter Ⅶ cw-complexes implicial complexes 2.cell decompositions 3.the notion of a cw-complex 4.subcomplexes 5.cell attaching 6.why cw-complexes are more fleble 7.yes, but...?Chapter Ⅷ construction of continuous functions on topologicalspaces 1.the urysohn lemma 2.the proof of the urysohn lemma 3.the tietze extension lemma 4.partitions of unity and vector bundle sections 5.paracompactnessChapter Ⅸ covering spaces 1.topological spaces over x 2.the concept of a covering space 3.path lifting 4.introduction to the classification of covering spaces 5.fundamental group and lifting behavior 6.the classification of covering spaces 7.covering transformations and universal cover 8.the role of covering spaces in mathematicsChapter Ⅹ the theorem of tychonoff 1.an unlikely theorem? 2.what is it good for? 3.the proof last Chapter set theory (by theodor br6cker) references table of symbolsindex
作者介绍
作者:(德)亚尼齐
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