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...
| Published in: | Springer eBooks |
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| Main Author: | |
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Series: | UNITEXT,
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1007/978-3-319-16958-3 Перейти в каталог НБ ТГУ |
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| 100 | 1 | |a Manetti, Marco. |e author. |9 328251 | |
| 245 | 1 | 0 | |a Topology |h electronic resource |c by Marco Manetti. |
| 260 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. |9 742221 | ||
| 300 | |a XII, 309 p. 72 illus. |b online resource. | ||
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| 490 | 1 | |a UNITEXT, |x 2038-5714 ; |v 91 | |
| 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 -- Homotopy -- 10 The fundamental group -- 11 Covering spaces -- Monodromy -- 12 van Kampen's theorem -- 13 Selected topics in algebraic topology -- 14 Hints and solutions -- 15 References -- 16 Index. | |
| 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; connectedness and compactness; Alexandrov compactification; quotient topologies; 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. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications. | ||
| 650 | 0 | |a mathematics. |9 566183 | |
| 650 | 0 | |a Algebraic topology. |9 566352 | |
| 650 | 1 | 4 | |a Mathematics. |9 566184 |
| 650 | 2 | 4 | |a Algebraic Topology. |9 566353 |
| 650 | 2 | 4 | |a Mathematics, general. |9 304764 |
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