Abstract

Observing that every Tychonofi space X has an exten- sion kX which is a weakly Lindelof space and the minimal quasi-F cover QF(kX) of kX is a weakly Lindelof, we show that 'kX : QF(kX) ! kX is a z # -irreducible map and that QF(flX) = flQF(kX). Using these, we prove that QF(kX) = kQF(X) if and only if ' k : kQF(X) ! kX is an onto map and flQF(X) = QF(flX).

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