Abstract
The star versions of the selection principle Ufin(O,Ω), namely Ufin⁎(O,Ω), SSfin⁎(O,Ω) and Ufin⁎(O,Ω) are studied. We explore ramifications concerning critical cardinalities. Quite a few interesting observations are obtained while dealing with the Isbell-Mrówka spaces, Niemytzki plane and Alexandroff duplicates. Properties like monotonically normal and locally countable cellularity (introduced here) play an important role in our investigation. We study games corresponding to Ufin(O,Ω) and its star variants which have not been investigated in prior works. Some open problems are posed.
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