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《拓撲空間(英文影印版)》是一部本科生學習拓撲空間的基礎教程。引導讀者很好的學習拓撲中有關幾何的東西什麼是最重要的。本書的內容分為三大部分，綫和麵、矩陣空間和拓撲空間，這些都將是為更進一步學習打下良好的基礎，在講解所熟悉領域的同時，自然而然地透露書不少新的知識點。書中將大量的數學詞匯概念囊括其中，不要求讀者對簡單定理或者集閤知識十分瞭解，從而減少讀者理解上的難度。收斂定理的應用在幫助讀者抓住重點的同時，逐漸接觸並理解拓撲的概念，書中的知識點步步逼近，前九節重在為本科生講述矩陣空間的知識，同時也包括瞭大量的材料，這些將成為研究生學習的教程。最後，書中講述瞭拓撲和諸多其他專題，如分析和集閤之間的聯係，通過總結部分，每章都增加瞭一些除瞭拓撲知識外的附加知識，這些豐富瞭內容，使得本書完備性更強。

preface
parr 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 mt. teac 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 tychonoffs theorem
extra: the axiom of choice
exercises
parr iv postscript
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
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