Topology / by Marco Manetti.

Format:

Book

Author/Creator:

Manetti, Marco.

Series:

La Matematica per il 3+2, 2038-5757 ; 153

Language:

English

Subjects (All):

Topology.

Local Subjects:

Topology.

Physical Description:

1 online resource (383 pages)

Edition:

2nd ed. 2023.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2023.

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.

Contents:

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.

Other Format:

Print version: Manetti, Marco Topology

ISBN:

3-031-32142-1