拓扑学导论：第二版 Introduction to Topology: Second Edition

基本信息

Series:Dover Books on Mathema 1.4tics

Format:Paperback / softback 256 pages

Publisher:Dover Publications Inc.

Imprint:Dover Publications Inc.

ISBN:9780486406800

Published:28 Mar 2003

Weight:376g

Dimensions:155 x 234 x 13 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

本书解释了度量空间拓扑在分析中的非平凡应用。它涵盖了度量空间、点集拓扑和代数拓扑，并包括练习、精选答案和 51 幅插图。1983 年版。

二十世纪数学中更重要的里程碑之一是拓扑学作为一个独立研究领域的发展，以及随后拓扑思想在其他数学领域的系统应用。虽然还有许多其他关于拓扑入门的著作，但本书采用的方法与其他教材略有不同。前两章讨论了度量空间和点集拓扑材料；后两章讨论了代数拓扑材料。

作者引导读者了解度量空间拓扑在分析中的许多非平凡应用，清楚地确立了拓扑与分析的相关性。其次，对初等代数拓扑主题的处理集中在具有具体几何意义的结果上，而代数形式相对较少；同时，这种处理方法也为一些非常不平凡的结果提供了证明。通过提出同伦理论而不考虑同调理论，重要的应用立即变得显而易见，而不需要大型正式程序。

先决条件是熟悉实数和一些基本的集合论。

精心挑选的练习被整合到文本中（作者为 Dover 版提供了选定练习的解决方案）。

书末列出了符号和参考书目。

Dover 因其出色的数学名单而广受认可，其中包括知名理论家，如 Paul J. Cohen（集合论和连续统假设）、Alfred Tarski（不可判定理论）、Gary Chartrand（入门图论）、Hermann Weyl（黎曼曲面的概念）、Shlomo Sternberg（动力系统）和 C. R. Wylie 在几何学方面的多部著作，以及 Stanley J. Farlow 的《科学家和工程师的偏微分方程》。

This text explains nontrivial applications of metric space topology to analysis. It covers metric space, point-set topology, and algebraic topology, and includes exercises, selected answers, and 51 illustrations. 1983 edition.

One of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics. While there are many other works on introductory topology, this volume employs a methodology somewhat different from other texts. Metric space and point-set topology material is treated in the first two chapters; algebraic topological material in the remaining two.

The authors lead readers through a number of nontrivial applications of metric space topology to analysis, clearly establishing the relevance of topology to analysis. Second, the treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning and presents relatively little algebraic formalism; at the same time, this treatment provides proof of some highly nontrivial results. By presenting homotopy theory without considering homology theory, significant applications become immediately evident without the necessity of a large formal program.

Prerequisites are familiarity with real numbers and some basic set theory.

Carefully chosen exercises are integrated into the text (the authors have provided solutions to selected exercises for the Dover edition).

A list of notations and bibliographical references appear at the end of the book.

Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.

作者简介

西奥多·威廉·甘林是一位美国数学家。他是加州大学洛杉矶分校数学名誉教授。

甘林出生于 1939 年。他于 1960 年获得耶鲁大学数学学士学位，并于 1963 年在加州大学伯克利分校获得博士学位。他的博士导师是 František Wolf。他的博士论文题为“C(X) 子空间中函数限制的扩展问题”。他于 1963 年至 1965 年担任麻省理工学院的 C.L.E. Moore 讲师，之后加入加州大学洛杉矶分校任教。

2012 年，他成为美国数学学会会员之一

Theodore William Gamelin is an American mathematician. He is a professor emeritus of mathematics at the University of California, Los Angeles.

Gamelin was born in 1939. He received his B.S. degree in mathematics from Yale University in 1960, and completed his Ph.D. at the University of California, Berkeley in 1963. His doctoral advisor was František Wolf. His doctoral dissertation was titled The extension problem for restrictions of functions in a subspace of C(X). He served as C.L.E. Moore Instructor at the Massachusetts Institute of Technology from 1963 to 1965, before joining the UCLA faculty.

In 2012, he became one of the inaugural Fellows of the American Mathematical Society