普通拓扑学
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- ISBN:9787506200578
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:711×1245/24开
- 页数:314
- 出版时间:2000-11-01
- 条形码:9787506200578 ; 978-7-5062-0057-8
内容简介
本书根据作者在芝加哥大学、加利福尼亚大学等高校讲授拓扑学的讲义编写而成,是一部经典研究生教材。作者在泛函分析和拓扑学领域颇有成就,有较广泛的影响力。目次:预备知识,①拓扑空间,②Moore-Smith收敛,③积空间和商空间④嵌入和度量化,⑤紧空间,⑥一致空间,⑦函数空间。
目录
CHAPTER O: PRELIMINARIES
SETS
SUBSETS AND COMPLEMENTS; UNION AND INTERSECTION .
Class calculus
RELATIONS
Relation calculus, equivalence relations
FUNCTIONS
ORDERINGS
Order-complete sets, chains, extension of order-preserving
functions
ALGEBRAIC CONCEPTS
THE REAL NUMBERS
Integers, definition by induction, b-adic expansions
COUNTABLE SETS
Subsets, unions, the set of real numbers
CARDINAL NUMBERS
Schroeder-Bernstein theorem
ORDINAL NUMBERS
The first uncountable ordinal
CARTESIAN PRODUCTS
HAUSDOKFF MAXIMAL PRINCIPLE
Maximal principle, Kuratowski-Zorn lemma, axiom of
choice, well-ordering principle
……
CHAPTER 1: TOPOLOGICAL SPACES
CHAPTER 2: MOORE-SMITH CONVERGENCE
CHAPTER 3: PRODUCT AND QUOTIENT SPACES
CHAPTER 4: EMBEDDING AND METRIZATION
CHAPTER 5: COMPACT SPACES
CHAPTER 6: UNIFORM SPACES
CHAPTER 7: FUNCTION SPACES
APPENDIX: ELEMENTARY SET THEORY
SETS
SUBSETS AND COMPLEMENTS; UNION AND INTERSECTION .
Class calculus
RELATIONS
Relation calculus, equivalence relations
FUNCTIONS
ORDERINGS
Order-complete sets, chains, extension of order-preserving
functions
ALGEBRAIC CONCEPTS
THE REAL NUMBERS
Integers, definition by induction, b-adic expansions
COUNTABLE SETS
Subsets, unions, the set of real numbers
CARDINAL NUMBERS
Schroeder-Bernstein theorem
ORDINAL NUMBERS
The first uncountable ordinal
CARTESIAN PRODUCTS
HAUSDOKFF MAXIMAL PRINCIPLE
Maximal principle, Kuratowski-Zorn lemma, axiom of
choice, well-ordering principle
……
CHAPTER 1: TOPOLOGICAL SPACES
CHAPTER 2: MOORE-SMITH CONVERGENCE
CHAPTER 3: PRODUCT AND QUOTIENT SPACES
CHAPTER 4: EMBEDDING AND METRIZATION
CHAPTER 5: COMPACT SPACES
CHAPTER 6: UNIFORM SPACES
CHAPTER 7: FUNCTION SPACES
APPENDIX: ELEMENTARY SET THEORY
展开全部
作者简介
John L. Kelley,加州大学伯克利分校(University of California, Berkeley)数学系教授,著有General Topology ,Measure and Integral,Linear Topological Spaces等多部研究生教材。
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