<電子ブック>
Topology : An Invitation / by K. Parthasarathy
(La Matematica per il 3+2. ISSN:20385757 ; 134)
版 | 1st ed. 2022. |
---|---|
出版者 | (Singapore : Springer Nature Singapore : Imprint: Springer) |
出版年 | 2022 |
本文言語 | 英語 |
大きさ | XVII, 267 p. 47 illus : online resource |
著者標目 | *Parthasarathy, K author SpringerLink (Online service) |
件 名 | LCSH:Topology LCSH:Mathematical analysis FREE:Topology FREE:Analysis |
一般注記 | 1 Aperitif: The Intermediate Value Theorem -- 2 Metric spaces -- 3 Topological spaces -- 4 Continuous maps -- 5 Compact spaces -- 6Topologies defined by maps -- 7 Products of compact spaces -- 8 Separation axioms -- 9 Connected spaces -- 10 Countability axioms This book starts with a discussion of the classical intermediate value theorem and some of its uncommon “topological” consequences as an appetizer to whet the interest of the reader. It is a concise introduction to topology with a tinge of historical perspective, as the author’s perception is that learning mathematics should be spiced up with a dash of historical development. All the basics of general topology that a student of mathematics would need are discussed, and glimpses of the beginnings of algebraic and combinatorial methods in topology are provided. All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincaré–Miranda, Brouwer’s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk’s antipodal theorem, the Borsuk–Ulam theorem andthe Lusternik–Schnirelmann–Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces. Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book HTTP:URL=https://doi.org/10.1007/978-981-16-9484-4 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9789811694844 |
|
電子リソース |
|
EB00228952 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA611-614.97 DC23:514 |
書誌ID | 4000141870 |
ISBN | 9789811694844 |