《拓扑空间(英文影印版)》是一部本科生学习拓扑空间的基础教程。引导读者很好的学习拓扑中有关几何的东西什么是最重要的。本书的内容分为三大部分，线和面、矩阵空间和拓扑空间。书中将大量的数学词汇概念囊括其中，不要求读者对简单定理或者集合知识十分了解，从而减少读者理解上的难度。收敛定理的应用在帮助读者抓住重点的同时，逐渐接触并理解拓扑的概念，书中的知识点步步逼近，前九节重在为本科生讲述矩阵空间的知识，同时也包括了大量的材料，这些将成为研究生学习的教程。本书由(美)布斯科斯著。

Preface

PART Ⅰ THE LINE AND THE PLANE

Chapter 1 What Topology Is About

 Topological Equivalence

 Continuity and Convergence

 A Few Conventions

 Extra: Topological Diversions

 Exercises

Chapter 2 Axioms for R

 Extra: Axiom Systems

 Exercises

Chapter 3 Convergent Sequences and Continuity

 Subsequences

 Uniform Continuity

 The Plane

 Extra: Bolzano (1781-1848)

 Exercises

ChaPter 4 Curves in the Plane

 Curves

 Homeomorphic Sets

 Brouwer's Theorem

 Extra: L.E.J. Brouwer (1881-1966)

PART Ⅱ METRI SPACES

Chapter 5 Metrics

 Extra: Camille Jordan (1838-1922)

 Exercises

Chapter 6 Open and Closed Sets

 Subsets of a Metric Space

 Collections of Sets

 Similar Metrics

 Interior and Closure

 The Empty Set

 Extra: Cantor (1845-1918)

 Exercises

Chapter 7 Completeness

 Extra: Meager Sets and the Mazur Game

 Exercises

Chapter 8 Uniform Convergence

 Extra: Spaces of Continuous Functions

 Exercises

Chapter 9 Sequential Compactness

 Extra: The p-adic Numbers

 Exercises

Chapter 10 Convergent Nets

 Inadequacy of Sequences

 Convergent Nets

 -Extra: Knots

 Exercises

Chapter 11 Transition to TOpology

 Generalized Convergence

 Topologies

 Extra: The Emergence of the Professional Mathematician

 Exercises

PART Ⅲ TOPOLOGICAL SPACES

Chapter 12 Topological Spaces

 Extra: Map Coloring

 Exercises

Chapter 13 Compactness and the Hausdorff Property

 Compact Spaces

 Hausdorff Spaces

 Extra: Hausdorff and the Measure Problem

 Exercises

Chapter 14 Products and Quotients

 Product Spaces

 Quotient Spaces

 Extra: Surfaces

 Exercises

Chapter 15 The Hahn-Tietze-Tong-Urysohn Theorems

 Urysohn's Lemma

 Interpolation and Extension

 Extra: Nonstandard Mathematics

 Exercises

Chapter 16 Connectedness

 Connected Spaces

 The Jordan Theorem

 Extra: Continuous Deformation of Curves

 Exercises

Chapter 17 Tvchonoffs Theorem

 Extra: The Axiom of Choice

 Exercises

PAler Ⅳ PosTsciuer

Chapter 18 A Smorgasbord for Further Study

 Countability Conditions

 Separation Conditions

 Compactness Conditions

 Compactifications

 Connectivity Conditions

 Extra: Dates from the History of General Topology

 Exercises

Chapter 19 Countable Sets

 Extra: The Continuum Hypothesis

A Farewell to the Reader

Literature

Index of Symbols

Index of Terms