UID:
almahu_9949552641002882
Umfang:
XIV, 377 p. 28 illus.
,
online resource.
Ausgabe:
2nd ed. 2023.
ISBN:
9783031321429
Serie:
La Matematica per il 3+2, 153
Inhalt:
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.
Anmerkung:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783031321412
Weitere Ausg.:
Printed edition: ISBN 9783031321436
Weitere Ausg.:
Printed edition: ISBN 9783031321443
Sprache:
Englisch
DOI:
10.1007/978-3-031-32142-9
URL:
https://doi.org/10.1007/978-3-031-32142-9
