03735nam 22007335 450 991014628470332120250801064930.03-540-68338-010.1007/BFb0096295(CKB)1000000000437361(SSID)ssj0000327310(PQKBManifestationID)12124859(PQKBTitleCode)TC0000327310(PQKBWorkID)10301600(PQKB)11785398(DE-He213)978-3-540-68338-4(MiAaPQ)EBC5592350(Au-PeEL)EBL5592350(OCoLC)1066195461(MiAaPQ)EBC6842177(Au-PeEL)EBL6842177(OCoLC)1113042792(PPN)155193465(EXLCZ)99100000000043736120121227d1997 u| 0engurnn#008mamaatxtccrTopics in Topology /by Stevo Todorcevic1st ed. 1997.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1997.1 online resource (VIII, 160 p.)Lecture Notes in Mathematics,1617-9692 ;1652Bibliographic Level Mode of Issuance: Monograph3-540-62611-5 Contents: Topology of pointwise convergence -- A theorem of Eberlein -- Ptak's Lemma -- Namioka's theorem -- Rosenthal's theorem -- Properties of Baire and Ramsey -- Baire property of analytic sets -- Baire property of filters and ideals -- Selective coideals -- Baire's characterization theorem and its corollaries -- Borel sets -- A selective analytic ideal -- Bourgain-Fremlin-Talagrand's theorem -- A space of ultrafilters -- Glazer's theorem -- A topological proof of van der Waerden theorem -- A semigroup of variable words -- Countable chain conditions of topological groups -- Michael's selection theorem -- Inverse systems -- Haydon's theorem -- Quotient groups -- A decomposition of compact groups -- Pestov's theorems -- Free topological groups -- Exponentially complete spaces -- Vaught's homeomorphism theorem -- Resolving a space: Accumulation orders and spectra -- Accumulation spectra of hyperspaces -- List of all exponentials -- Multiplication of accumulation orders.The book describes some interactions of topology with other areas of mathematics and it requires only basic background. The first chapter deals with the topology of pointwise convergence and proves results of Bourgain, Fremlin, Talagrand and Rosenthal on compact sets of Baire class-1 functions. In the second chapter some topological dynamics of beta-N and its applications to combinatorial number theory are presented. The third chapter gives a proof of the Ivanovskii-Kuzminov-Vilenkin theorem that compact groups are dyadic. The last chapter presents Marjanovic's classification of hyperspaces of compact metric zerodimensional spaces.Lecture Notes in Mathematics,1617-9692 ;1652TopologyTopological groupsLie groupsFunctions of real variablesTopologyTopological Groups and Lie GroupsReal FunctionsTopology.Topological groups.Lie groups.Functions of real variables.Topology.Topological Groups and Lie Groups.Real Functions.51454C30mscTodorcevic Stevo61532MiAaPQMiAaPQMiAaPQBOOK9910146284703321Topics in topology262434UNINA