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Topology

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Topology/ by Marco Manetti.
作者:	Manetti, Marco.
面頁冊數:	XII, 309 p. 72 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebraic topology. -
電子資源:	https://doi.org/10.1007/978-3-319-16958-3
ISBN:	9783319169583

Topology
Manetti, Marco.

Topology[electronic resource] /by Marco Manetti. - 1st ed. 2015. - XII, 309 p. 72 illus.online resource. - La Matematica per il 3+2,912038-5722 ;. - La Matematica per il 3+2,84.

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.

ISBN: 9783319169583

Standard No.: 10.1007/978-3-319-16958-3doiSubjects--Topical Terms:

678206
Algebraic topology.

LC Class. No.: QA612-612.8

Dewey Class. No.: 514.2

Topology
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