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...
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
Cham
Springer Nature Switzerland
2023, 2023
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Edition: | 2nd ed. 2023 |
Series: | La Matematica per il 3+2
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Summary: | 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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Physical Description: | XIV, 377 p. 28 illus online resource |
ISBN: | 9783031321429 |