Topology / / by Marco Manetti
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| Autore: |
Manetti Marco
|
| Titolo: |
Topology / / by Marco Manetti
|
| Pubblicazione: | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Edizione: | 2nd ed. 2023. |
| Descrizione fisica: | 1 online resource (383 pages) |
| Disciplina: | 514 |
| Soggetto topico: | Topology |
| Nota di contenuto: | 1 Geometrical introduction to topology -- 2 Sets -- 3 Topological structures -- 4 Connectedness and compactness -- 5 Topological quotients -- 6 Sequences -- 7 Manifolds, infinite products and paracompactness -- 8 More topics in general topology -- 9) Intermezzo -- 10 Homotopy -- 11 The fundamental group -- 12 Covering spaces -- 13 Monodromy -- 14 van Kampen's theorem -- 15 A topological view of sheaf cohomology -- 16 Selected topics in algebraic topology -- 17 Hints and solutions. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Topology |
| ISBN: | 3-031-32142-1 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910743688903321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
La Matematica per il 3+2, . 2038-5757 ; ; 153