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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Resolutions of $ H$-closed spaces


Author: Louis M. Friedler
Journal: Proc. Amer. Math. Soc. 71 (1978), 309-312
MSC: Primary 54D25
MathSciNet review: 0493965
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0493965-1
PII: S 0002-9939(1978)0493965-1
Article copyright: © Copyright 1978 American Mathematical Society