LEADER 03448nam 2200649 450 001 996466606403316 005 20220911152213.0 010 $a3-540-68338-0 024 7 $a10.1007/BFb0096295 035 $a(CKB)1000000000437361 035 $a(SSID)ssj0000327310 035 $a(PQKBManifestationID)12124859 035 $a(PQKBTitleCode)TC0000327310 035 $a(PQKBWorkID)10301600 035 $a(PQKB)11785398 035 $a(DE-He213)978-3-540-68338-4 035 $a(MiAaPQ)EBC5592350 035 $a(Au-PeEL)EBL5592350 035 $a(OCoLC)1066195461 035 $a(MiAaPQ)EBC6842177 035 $a(Au-PeEL)EBL6842177 035 $a(OCoLC)1113042792 035 $a(PPN)155193465 035 $a(EXLCZ)991000000000437361 100 $a20220911d1997 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTopics in topology /$fStevo Todorcevic 205 $a1st ed. 1997. 210 1$aBerlin, Germany :$cSpringer-Verlag,$d[1997] 210 4$dİ1997 215 $a1 online resource (VIII, 160 p.) 225 1 $aLecture Notes in Mathematics ;$v1652 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-62611-5 327 $aContents: 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. 330 $aThe book describes some interactions of topology with other areas of mathematics and it requires only basic background. The first chapter deals with the topology of pointwise convergence and proves results of Bourgain, Fremlin, Talagrand and Rosenthal on compact sets of Baire class-1 functions. In the second chapter some topological dynamics of beta-N and its applications to combinatorial number theory are presented. The third chapter gives a proof of the Ivanovskii-Kuzminov-Vilenkin theorem that compact groups are dyadic. The last chapter presents Marjanovic's classification of hyperspaces of compact metric zerodimensional spaces. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1652. 606 $aTopology 606 $aTopological groups 606 $aFunctions of real variables 615 0$aTopology. 615 0$aTopological groups. 615 0$aFunctions of real variables. 676 $a514 686 $a54C30$2msc 700 $aTodorcevic$b Stevo$061532 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466606403316 996 $aTopics in topology$9262434 997 $aUNISA