MINIMAL QUASI-F COVERS OF REALCOMPACT SPACES
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.In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman com pactification of the inverse image Φ-1K(X) of the space X under the covering map ΦK QFK→K. Using these, we show that for any space X, βQFX = QFβυX and that a realcompact space X is a projective object in the category Rcomp# of all realcompact spaces and their z#-irreducible maps if and only if X is a quasi-F space.
Abstract
.In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman com pactification of the inverse image Φ-1K(X) of the space X under the covering map ΦK QFK→K. Using these, we show that for any space X, βQFX = QFβυX and that a realcompact space X is a projective object in the category Rcomp# of all realcompact spaces and their z#-irreducible maps if and only if X is a quasi-F space.
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