|We consider the Katuta-Junnila problem.|
Is a space metacompact if every directed open cover of the space has a
Is a space submetacompact if every directed open cover of the space
has a $sigma$-cushioned refinement?
We summarize some previous known partial results and present an affirmative answer
to problem 1 in the class of strongly first countable spaces.
metacompact, submetacompact, $(sigma)$-closure-preserving, $(sigma$)-cushioned.
Math Review Classification
Primary 54B10, 54D20
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