普通拓扑学(英文版)

本书作者在泛函分析和 拓扑学领域很有成就，著 作颇多，有较广泛的影响 。本书是根据作者在芝加 哥大学、加利福尼亚大学 等处讲授拓扑学的讲义编 写而成的，是一本优秀的 教材。 本书包含了，预备知识 ，拓扑空间，Moore-Smith 收敛，积空间和商空间， 嵌入和度量化，紧空间， 一致空间，函数空间等内 容。

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