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Topology. 2nd ed. 2023.
・ISBN 978-3-031-32141-2 paper EUR 69.99
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| 著者・編者 | Manetti, Marco, |
|---|---|
| シリーズ | UNITEXT |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2023 |
| ページ数 | 377 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-2720＞ |
解説
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; con- nectedness and compactness; Alexandrov compactification; quotient topol- ogies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced.
This second edition contains a new chapter with a topological introduction to sheaf cohomology and applications.It also corrects some inaccuracies and some additional exercises are proposed.
The textbook is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.