MINIMAL QUASI-F COVERS OF SOME EXTENSION
MINIMAL QUASI-F COVERS OF SOME EXTENSION
Observing that every Tychonoff space X has an extension <TEX>$kX$</TEX> which is a weakly Lindel<TEX>$\ddot{o}$</TEX>f space and the minimal quasi-F cover <TEX>$QF(kX)$</TEX> of <TEX>$kX$</TEX> is a weakly Lindel<TEX>$\ddot{o}$</TEX>f, we show that <TEX>${\Phi}_{kX}:QF(kX){\rightarrow}kX$</TEX> is a <TEX>$z^{\sharp}$</TEX>-irreducible map and that <TEX>$QF({\beta}X)=QF(kX)$</TEX>. Using these, we prove that <TEX>$QF(kX)=kQF(X)$</TEX> if and only if <TEX>${\Phi}^k_X:kQF(X){\rightarrow}kX$</TEX> …