拓扑空间

《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，这些都将是为更进一步学习打下良好的基础，在讲解所熟悉领域的同时，自然而然地透露书不少新的知识点。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。最后，书中讲述了拓扑和诸多其他专题，如分析和集合之间的联系，通过总结部分，每章都增加了一些除了拓扑知识外的附加知识，这些丰富了内容，使得本书完备性更强。

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