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＜E-Book＞
Topology / by Marco Manetti
(La Matematica per il 3+2. ISSN:20385757 ; 91)

Edition	1st ed. 2015.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2015
Language	English
Size	XII, 309 p. 72 illus : online resource
Authors	*Manetti, Marco author SpringerLink (Online service)
Subjects	LCSH:Algebraic topology LCSH:Mathematics FREE:Algebraic Topology FREE:Mathematics
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-16958-3

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