- 拓扑学(英文版)
- - 作者：(德)亚尼齐|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787510040641
  - 出版日期：2012/01/01
  - 页数：192
- 售价：19.6

内容大纲
《拓扑学》是一部学习拓扑的本科生入门书籍。点集拓扑是本书的重点，尤其对非专业人士来说更为重要。本书的讲述方式新颖，这种非传统的表达方式更适合初学者学习理解。图表贯穿于本书的始终，这样更有利于培养读者的感性认识，例子更好地帮助读者理解本书的核心基本拓扑问题，这些都是更深入学习拓扑和几何问题的关键。
作者介绍
目录
Introduction
  1. What is point-set topology about?
  2. Origin and beginnings
CHAPTER I Fundamental Concepts
  l. The concept of a topological space
  2. Metric spaces
  3. Subspaces, disjoint unions and products
  4. Bases 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
  I. 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 Tyehonoff
  1. An unlikely theorem?
  2. What is it good for?
  3. The proof
LAST CHAPTER
Set Theory (by Thcodor Brfcker)
References
Table of Symbols
Index

内容大纲

作者介绍

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