Resolutions of 𝐻-closed spaces

Friedler, Louis M.

doi:10.1090/S0002-9939-1978-0493965-1

Resolutions of $H$-closed spaces
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by Louis M. Friedler

Proc. Amer. Math. Soc. 71 (1978), 309-312

DOI: https://doi.org/10.1090/S0002-9939-1978-0493965-1

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Abstract:

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

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