Minimal covers and filter spaces

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 ΛX are given by the filter space of fixed Z(X)#-ultrafilters on X and that of fixed σZ(X)#-ultrafilters on X, respectively. We also show that for a weakly Lindelöf space X, βΛX and ΛβX are homeomorphic.