MINIMAL QUASI-F COVERS OF SOME EXTENSION

Abstract

Observing that every Tychonoff space X has an extension kX which is a weakly Lindel¨of space and the minimal quasi-F cover QF (kX) of kX is a weakly Lindel¨of, we show that ΦkX : QF (kX) → kX is a z#-irreducible map and that QF (βX) = βQF (kX). Using these, we prove that QF (kX) = kQF (X) if and only if Φk X : kQF (X) → kX is an onto map and βQF (X) = QF (βX).

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