COCOMPACT F-BASES AND RELATION BETWEEN COVER AND COMPACTIFICATION

Observing that a locally weakly Lindel$\"{o}$f space is a quasi-F space if and only if it has an F-base, we show that every dense weakly Lindel$\"{o}$f subspace of an almost-p-space is C-embedded, every locally weakly Lindel$\"{o}$f space with a cocompact F-base is a locally compact and quasi-F space and that if Y is a dense weakly Lindel$\"{o}$f subspace of X which has a cocompact F-base, then $\beta$Y and X are homeomorphic. We also show that for any a separating nest generated intersection ring F on a space X, there is a separating nest generated intersection ring g on $\phi_{Y}^{-1}$(X) such that QF(w(X, F)) and ($\phi_{Y}^{-1}$(X),g) are homeomorphic and $\phi_{Y}_{x}$(g$^#$)=F$^#$.