LEADER 03040nam 22004815 450 001 9910743688903321 005 20251009083512.0 010 $a3-031-32142-1 024 7 $a10.1007/978-3-031-32142-9 035 $a(MiAaPQ)EBC30727003 035 $a(Au-PeEL)EBL30727003 035 $a(DE-He213)978-3-031-32142-9 035 $a(PPN)272735337 035 $a(CKB)28141357800041 035 $a(EXLCZ)9928141357800041 100 $a20230901d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTopology /$fby Marco Manetti 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (383 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v153 311 08$aPrint version: Manetti, Marco Topology Cham : Springer,c2023 9783031321412 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 -- 10 Homotopy -- 11 The fundamental group -- 12 Covering spaces -- 13 Monodromy -- 14 van Kampen's theorem -- 15 A topological view of sheaf cohomology -- 16 Selected topics in algebraic topology -- 17 Hints and solutions. 330 $aThis is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; con- nectedness and compactness; Alexandrov compactification; quotient topol- ogies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. This second edition contains a new chapter with a topological introduction to sheaf cohomology and applications.It also corrects some inaccuracies and some additional exercises are proposed. The textbook is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v153 606 $aTopology 606 $aTopology 615 0$aTopology. 615 14$aTopology. 676 $a514 700 $aManetti$b Marco$0308374 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910743688903321 996 $aTopology$91522618 997 $aUNINA