Abstract
It is shown that every Hausdorff space X is the perfect, irreducible, continuous image of a Hausdorff space X ~ \tilde X which has a basis with open closures. Further, w ( X ~ ) ⩽ w ( X ) w(\tilde X) \leqslant w(X) , where w ( X ~ ) w(\tilde X) represents the weight of X, and if X is H-closed then X ~ \tilde X is also H-closed. A corollary of this result is that if f : X → Y f:X \to Y is a continuous map of the H-closed space X onto the semi-regular Hausdorff space Y, then w ( Y ) ⩽ w ( X ) w(Y) \leqslant w(X) .
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