书目名称 | General Topology | 编辑 | Jacques Dixmier | 视频video | | 丛书名称 | Undergraduate Texts in Mathematics | 图书封面 |  | 描述 | This book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer sity year). The course was taught during the first semester of the 1979-80 academic year (three hours a week of lecture, four hours a week of guided work). Topology is the study of the notions of limit and continuity and thus is, in principle, very ancient. However, we shall limit ourselves to the origins of the theory since the nineteenth century. One of the sources of topology is the effort to clarify the theory of real-valued functions of a real variable: uniform continuity, uniform convergence, equicontinuity, Bolzano-Weierstrass theorem (this work is historically inseparable from the attempts to define with precision what the real numbers are). Cauchy was one of the pioneers in this direction, but the errors that slip into his work prove how hard it was to isolate the right concepts. Cantor came along a bit later; his researches into trigonometric series led him to study in detail sets of points of R (whence the concepts of open set and closed set in R, which in his work are intermingled with much subtler concepts). The foregoi | 出版日期 | Textbook 1984 | 关键词 | Cantor; Compact space; Connected space; Finite; Topology; function; theorem; variable | 版次 | 1 | doi | https://doi.org/10.1007/978-1-4757-4032-5 | isbn_softcover | 978-1-4419-2823-8 | isbn_ebook | 978-1-4757-4032-5Series ISSN 0172-6056 Series E-ISSN 2197-5604 | issn_series | 0172-6056 | copyright | Springer Science+Business Media New York 1984 |
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