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Chapter1
Preliminaries
Thischaptercontainsbackgroundmaterialwhichisnecessarytounder-
standfurtherpartsofthismonograph.Thematerialisdividedintothree
sectionsconcerningselectedtopicsofsettheory,topologyandmeasure
theory.Thereisassumedthatthereaderhastheuniversityknowledgein
eachofthissubjects,butdespitethisineachsectiononefindsselecteddef-
initionsandfacts(i.e.,theoremswithoutproofs)thereforeinnowayshould
thischapterbetreatedasacourseonanymentionedsubject,butratheras
areminderofknownfactsandnotions.
Aftereachsectionthereareprovidedbibliographicandhistoricalnotes
tostandardtextbooksandmonographs,wherethereadercanfindmore
information,fullproofs,examples,etc.
Sometimes,resultscitedinthischapterareformulatedinaformwhich
ismoreconvenienttofurtherpartsofthismonograph,butdifferentfrom
theonesgiveninthereferences.However,itiseasilyderivedfromtheform
giveninthereferences.
101Selectedfactsofsettheory
Ifnotassumedotherwise,sincenowitisassumedthatκisaregularun-
countablecardinalnumberandRisasubsetofκ.Itisalsoassumedthat
basicdefinitionsandfactsconcerningsettheoryareknown.Thereforeonly
someofthemareremindedhere.
