Manetti Topology

Erscheinungsjahr 2015
ISBN: 978-3-319-16958-3
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 91, 309 Seiten, eBook

Reihe: UNITEXT

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; connectedness and compactness; Alexandrov compactification; quotient topologies; 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. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Manetti, Marco

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.- Homotopy.- 10 The fundamental group.- 11 Covering spaces.- Monodromy.- 12 van Kampen's theorem.- 13 Selected topics in algebraic topology.- 14 Hints and solutions.- 15 References.- 16 Index.

Über Autor(innen)

Prof.
Marco Manetti
, Dipartimento di Matematica "Guido Castelnuovo", Sapienza - Università di Roma, Roma, Italy.