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On ▫$M$▫-separability of countable spaces and function spaces
Repovš, Dušan, 1954- ; Zdomskyy, Lyubomyr, 1983-
V članku proučujemo ▫$M$▫-separabilnost in tudi druge kombinatorične verzije separabilnosti. Konkretno, dokažemo, da iz domneve ▫$\mathfrak{b=d}$▫ v teoriji množic sledi, da razred selektivno ...separabilnih prostorov ni zaprt za operacijo končnih produktov, celo za prostore zveznih funkcij s topologijo konvergence po točkah. Dokažemo tudi, da v modelu Frankiewicza, Shelaha in Zbierskega ne obstaja maksimalen ▫$M$▫-separabilen števen prostor, v katerem vsezaprte ▫$P$▫-podmnožice prostora ▫$\omega^\ast$▫ dopuščajo obstoj neštevne družine nepraznih paroma disjunktnih podmnožic. To daje odgovor na več vprašanj, ki so jih zastavili Bella, Bonanzinga, Matveev in Tkachuk.
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