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Topology

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Topology/ by Marco Manetti.
Author:	Manetti, Marco.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	xiv, 377 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Topology. -
Online resource:	https://doi.org/10.1007/978-3-031-32142-9
ISBN:	9783031321429

Topology
Manetti, Marco.

Topology[electronic resource] /by Marco Manetti. - Second edition. - Cham :Springer Nature Switzerland :2023. - xiv, 377 p. :ill., digital ;24 cm. - La matematica per il 3+2,v. 1532038-5757 ;. - La matematica per il 3+2 ;v.111..

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.

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.

ISBN: 9783031321429

Standard No.: 10.1007/978-3-031-32142-9doiSubjects--Topical Terms:

633483
Topology.

LC Class. No.: QA611 / .M3613 2023

Dewey Class. No.: 514

Topology
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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.
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.
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