拓撲學（簡體書）

亞尼齊編著的《拓撲學》內容介紹：This volume covers approximately 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.本書是一部學習拓撲的本科生入門書籍。點集拓撲是本書的重點，尤其對非專業人士來說更是十分的重要。本書的講述方式新穎，非傳統的表達方式更適合初學者學習理解。圖表貫穿於本書的始終，這樣更有利於培養讀者的感性認識，例子則更好幫助讀者理解本書的核心基本拓撲問題，這些都是更深入學習拓撲和幾何問題的關鍵。目次：引論；基本概念；拓撲向量空間；商拓撲；矩陣空間完備化；同倫；兩個可數性公理；CW-複雜性；拓撲空間上的連續函數結構；覆蓋空間；Tychonoff定理；集合理論。
讀者對象；數學專業的本科生、研究生和相關專業的教師。

作者:(德)亞尼齊

亞尼齊編著的《拓撲學》內容介紹：This volume covers approximately the amount of point-set topology that a student who does not intend to specialize in the field should nevertheless know.This is not a whole lot, and in condensed form would occupy perhaps only a small booklet. Our aim, however, was not economy of words, but a lively presentation of the ideas involved, an appeal to intuition in both the immediate and the higher meanings.

Introduction
1.what is point-set topology about?
2.origin and beginnings
Chapter 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 axiom
8.compactness
Chapter 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 examples
Chapter 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 together
Chapter Ⅳ completion of metric spaces
1.the completion of a metric space
2.completion of a map
3.completion of normed spaces
Chapter 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 axioms
1.first and second countability axioms
2.infinite products
3.the role of the countability axioms
Chapter Ⅶ cw-complexes
1.simplicial complexes
2.cell decompositions
3.the notion of a cw-complex
4.subcomplexes
5.cell attaching
6.why cw-complexes are more flexible
7.yes, but...?
Chapter Ⅷ construction of continuous functions on topological spaces
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.paracompactness
Chapter 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 mathematics
Chapter 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 symbols
index