Topology by Marco ManettiTopology by Marco Manetti

Topology

byMarco Manetti

Paperback | June 5, 2015

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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.

Prof.Marco Manetti , Dipartimento di Matematica "Guido Castelnuovo", Sapienza - Università di Roma, Roma, Italy.
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Title:TopologyFormat:PaperbackDimensions:309 pagesPublished:June 5, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319169572

ISBN - 13:9783319169576

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Table of 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.- 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.