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 $eta$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$^#$.