Abstract
Observing that a locally weakly Lindelöf space X is a quasi-F space (basically disconnected space respectively) if and only if it has an F-base (pretty base respectively), we show that for a locally weakly Lindelöf space X, its minimal quasi-F cover QF (X) and minimal basically disconnected cover Λ X are given by the filter space of fixed Z(X) #-ultrafilters on X and that of fixed σ Z(X) #-ultrafilters on X, respectively. We also show that for a weakly Lindelöf space X, βΛ X and Λβ X are homeomorphic.
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