Marco Manetti: Topology | Taschenbuch

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Cover: 9783031321412 | Topology | Marco Manetti | Taschenbuch | La Matematica per il 3+2

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

Provides a comprehensive treatment of the basic theory and of some complementary topics

Contains lots of exercises, of various difficulty level

Contains an original topological approach to sheaf cohomology

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2023
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	392
Reihe:	La Matematica per il 3+2
Inhalt:	xiv 377 S. 28 s/w Illustr. 377 p. 28 illus.
ISBN-13:	9783031321412
ISBN-10:	3031321413
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Manetti, Marco
Auflage:	2nd ed. 2023
Hersteller:	Springer Nature Switzerland Springer International Publishing AG La Matematica per il 3+2
Maße:	235 x 155 x 20 mm
Von/Mit:	Marco Manetti
Erscheinungsdatum:	03.09.2023
Gewicht:	0,664 kg

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