| Titre : |
Topology |
| Type de document : |
texte imprimé |
| Auteurs : |
Marco Manetti, Auteur |
| Mention d'édition : |
2éd. |
| Editeur : |
France: Springer Nature Switzerland AG |
| Année de publication : |
2023 |
| Collection : |
Unitext, ISSN 20385722 |
| Importance : |
377p. |
| Présentation : |
Couverture externe,figures |
| Format : |
24X16cm |
| ISBN/ISSN/EAN : |
978-3-031-32141-2 |
| Note générale : |
Marco Manetti (born 1966) is full professor in geometry at Sapienza University of Rome (Italy). His research activity concerns algebraic geometry, deformation theory and higher algebraic structures. He is author of the books "Topologia'' (Italian, 2008,2014), "Topology'' (2015) and "Lie methods in deformation theory'' (2022), all of them published with Springer.
Index:p.373 |
| Langues : |
Anglais moyen (ca.1100-1500) (enm) Langues originales : Anglais moyen (ca.1100-1500) (enm) |
| Catégories : |
2 Science
|
| Mots-clés : |
Topolody,sets,topological structures |
| Index. décimale : |
514 |
| 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. |
| Note de contenu : |
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 |
Topology [texte imprimé] / Marco Manetti, Auteur . - 2éd. . - [S.l.] : France: Springer Nature Switzerland AG, 2023 . - 377p. : Couverture externe,figures ; 24X16cm. - ( Unitext, ISSN 20385722) . ISBN : 978-3-031-32141-2 Marco Manetti (born 1966) is full professor in geometry at Sapienza University of Rome (Italy). His research activity concerns algebraic geometry, deformation theory and higher algebraic structures. He is author of the books "Topologia'' (Italian, 2008,2014), "Topology'' (2015) and "Lie methods in deformation theory'' (2022), all of them published with Springer.
Index:p.373 Langues : Anglais moyen (ca.1100-1500) ( enm) Langues originales : Anglais moyen (ca.1100-1500) ( enm)
| Catégories : |
2 Science
|
| Mots-clés : |
Topolody,sets,topological structures |
| Index. décimale : |
514 |
| 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. |
| Note de contenu : |
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 |
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