拓扑学(英文版)
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作者(德)亚尼齐|责编:刘慧//高蓉
出版社世界图书出版公司
ISBN9787510040641
出版时间2012-01
装帧平装
开本其他
定价49元
货号30924410
上书时间2024-10-12
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作者简介
作者-(德)亚尼齐...
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
内容摘要
《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。
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