| We consider the Katuta-Junnila problem. begin{enumerate} item Is a space metacompact if every directed open cover of the space has a cushioned refinement? item 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. |
Keywords
metacompact, submetacompact, $(sigma)$-closure-preserving, $(sigma$)-cushioned.
Math Review Classification
Primary 54B10, 54D20
Last Updated
24/3/97
Length
14 pages
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