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.
Tabella dei contenuti
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.
Circa l’autore
Prof. Marco Manetti, Dipartimento di Matematica ‘Guido Castelnuovo’, Sapienza – Università di Roma, Roma, Italy.
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