LEADER 03443nam 22006255 450 001 9910299773303321 005 20200703104145.0 010 $a3-319-16958-0 024 7 $a10.1007/978-3-319-16958-3 035 $a(CKB)3710000000430778 035 $a(SSID)ssj0001558645 035 $a(PQKBManifestationID)16182750 035 $a(PQKBTitleCode)TC0001558645 035 $a(PQKBWorkID)14818714 035 $a(PQKB)10772185 035 $a(DE-He213)978-3-319-16958-3 035 $a(MiAaPQ)EBC6314374 035 $a(MiAaPQ)EBC5590891 035 $a(Au-PeEL)EBL5590891 035 $a(OCoLC)911924242 035 $a(PPN)186400470 035 $a(EXLCZ)993710000000430778 100 $a20150528d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTopology /$fby Marco Manetti 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XII, 309 p. 72 illus.) 225 1 $aLa Matematica per il 3+2,$x2038-5722 ;$v91 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-16957-2 327 $a1 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. 330 $aThis is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications. 410 0$aLa Matematica per il 3+2,$x2038-5722 ;$v91 606 $aAlgebraic topology 606 $aMathematics 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009 615 0$aAlgebraic topology. 615 0$aMathematics. 615 14$aAlgebraic Topology. 615 24$aMathematics, general. 676 $a514.2 700 $aManetti$b Marco$4aut$4http://id.loc.gov/vocabulary/relators/aut$0308374 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299773303321 996 $aTopology$91522618 997 $aUNINA