【2014新书】点集拓扑教程

John B. Conway, "A Course in Point Set Topology"
English | ISBN: 3319023675 | 2014 | 144 pages | PDF | 3 MB

【作者简介】
John B. Conway为The George Washington University数学荣退教授。此牛的另外一本经典教材《泛函分析教程》，引无数英雄竞折腰。此牛一生没上过类似中国的985大学甚至211大学，但在泛函分析领域做出了突出贡献。

【教材简介】
前一阵子，论坛热炒一低调的南大毕业生，此牛犊子在研究生期间就发表了若干SSCI文章，此牛犊子数学功底甚好，拓扑对他应是小菜。如果你也想象他一样，先看看点集拓扑。这是拓扑中最简单的部分。

This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.

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