03443nam 22006255 450 991029977330332120200703104145.03-319-16958-010.1007/978-3-319-16958-3(CKB)3710000000430778(SSID)ssj0001558645(PQKBManifestationID)16182750(PQKBTitleCode)TC0001558645(PQKBWorkID)14818714(PQKB)10772185(DE-He213)978-3-319-16958-3(MiAaPQ)EBC6314374(MiAaPQ)EBC5590891(Au-PeEL)EBL5590891(OCoLC)911924242(PPN)186400470(EXLCZ)99371000000043077820150528d2015 u| 0engurnn|008mamaatxtccrTopology /by Marco Manetti1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (XII, 309 p. 72 illus.) La Matematica per il 3+2,2038-5722 ;91Bibliographic Level Mode of Issuance: Monograph3-319-16957-2 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.La Matematica per il 3+2,2038-5722 ;91Algebraic topologyMathematicsAlgebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Mathematics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/M00009Algebraic topology.Mathematics.Algebraic Topology.Mathematics, general.514.2Manetti Marcoauthttp://id.loc.gov/vocabulary/relators/aut308374MiAaPQMiAaPQMiAaPQBOOK9910299773303321Topology1522618UNINA