A note on disrete sets
Comment.Math.Univ.Carolin. 50,3 (2009)463{475.
Abstrat: We give several partial positive answersto a question of Juhasz and Szent-
miklossy regarding the minimum number of disrete sets required to over a ompat
spae. We studythe relationship between the size of disrete sets, free sequenes and
their losureswiththe ardinality ofaHausdorspae, improvingknownresults inthe
literature.
Keywords: disrete set, dispersion harater, ompat spae, Eberlein ompat, free
sequene,elementarysubmodel
AMSSubjetClassiation:54A25
Referenes
[1℄ AlasO.,Onlosuresofdisretesubsets,QuestionsAnswersGen.Topology20(2002),85{89.
[2℄ Alas O., Tkahuk V., WilsonR., Closures of disrete setsoften reet global properties,
TopologyPro.25(2000),Spring,27{44.
[3℄ Arhangel'skiiA.V.,Strutureandlassiationoftopologialspaesandardinalinvariants,
RussianMath.Surveys33(1978),33{96.
[4℄ DowA.,Anintrodutiontoappliationsofelementarysubmodelstotopology,TopologyPro.
13(1988),no.1,17{72.
[5℄ DowA., Closures of disrete setsin ompat spaes,Studia Math. Si.Hung. 42(2005),
227{234.
[6℄ EngelkingR.,GeneralTopology,seonded.,SigmaSeriesinPureMathematis,no.6,Hel-
dermannVerlag,Berlin,1989.
[7℄ GerlitsJ.,Ona problemofS.Mrowka,Period.Math.Hungar.4(1973),71{80.
[8℄ GerlitsJ.,Ona generalizationofdyadiity,StudiaSi.Math.Hungar.13(1978),1{17.
[9℄ GerlitsJ.,JuhaszI.,SzentmiklossyZ.,TwoimprovementsonTkahenko'sadditiontheorem,
Comment.Math.Univ.Carolin.,46(2005),no.4,705{710.
[10℄ GruenhageG.,Generalizedmetrispaes,inHandbookofSetTheoretiTopology,K.Kunen
andJ.E.Vaughan,Eds.,North-Holland,Amsterdam,1984.
[11℄ GruenhageG.,AnoteonGul'koompatspaes,Pro.Amer.Math.So.100(1987),371{
376.
[12℄ GruenhageG.,Coveringompatabydisreteandotherseparatedsets,preprint.
[13℄ JuhaszI.,Cardinal Funtionin Topology -TenYearsLater,MathematialCentreTrats,
123,MathematishCentrum,Amsterdam,1980.
[14℄ JuhaszI.,vanMillJ.,Coveringompatabydisretesubspaes,TopologyAppl.154(2007),
283{286.
[15℄ I.Juhasz,Z.Szentmiklossy,Astrengtheningofthe
Ceh-Pospisiltheorem,preprint.
[16℄ LeidermanA.,SokolovG.,AdequatefamiliesofsetsandCorsonompats,Comment.Math.
Univ.Carolin.25(1984),no.2,233{246.
[17℄ Ridderbos G.J.,Powerhomogeneityintopology,DotoralThesis,VrijeUniversiteit,Ams-
terdam,2007.
[18℄ SpadaroS.,Coveringbydisreteandlosed disretesets,TopologyAppl.156(2009),721{
727.
[19℄ WatsonS.,Loallyompat normal spaes in theonstrutibleuniverse,Canad. J.Math.,
vol.XXXIV,no.5,1982,1091{1096.
[20℄ YakovlevN.,Onbiompatain-produtsandrelated spaes,Comment.Math.Univ.Car-
olin.21(1980),no.2,263{283.
