Topology
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...
Saved in:
| Main Author | |
|---|---|
| Format | Electronic eBook |
| Language | English |
| Published |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2023.
|
| Edition | 2nd ed. 2023. |
| Series | La Matematica per il 3+2,
153. |
| Subjects | |
| Online Access | Full text |
| ISBN | 9783031321429 9783031321412 |
| ISSN | 2038-5757 ; |
| Physical Description | 1 online zdroj (383 stran). |
Cover
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| 100 | 1 | |a Manetti, Marco. | |
| 245 | 1 | 0 | |a Topology / |c by Marco Manetti. |
| 250 | |a 2nd ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online zdroj (383 stran). | ||
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| 490 | 1 | |a La Matematica per il 3+2, |x 2038-5757 ; |v 153 | |
| 505 | 0 | |a 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. | |
| 506 | |a Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty | ||
| 520 | |a 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. | ||
| 650 | 0 | |a Topology. | |
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| 776 | 0 | 8 | |i Print version: |a Manetti, Marco |t Topology |d Cham : Springer,c2023 |z 9783031321412 |
| 830 | 0 | |a La Matematica per il 3+2, |x 2038-5757 ; |v 153. | |
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