| Titre : |
Topology |
| Type de document : |
texte imprimé |
| Auteurs : |
Marco Manetti, Auteur |
| Mention d'édition : |
2éd |
| Editeur : |
Springer International Publishing AG |
| Année de publication : |
2023 |
| Importance : |
377 p |
| Format : |
24 x 16 cm |
| ISBN/ISSN/EAN : |
978-3-031-32141-2 |
| Langues : |
Anglais (eng) |
| Résumé : |
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. |
Topology [texte imprimé] / Marco Manetti, Auteur . - 2éd . - [S.l.] : Springer International Publishing AG, 2023 . - 377 p ; 24 x 16 cm. ISBN : 978-3-031-32141-2 Langues : Anglais ( eng)
| Résumé : |
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. |
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Topology
