Abstract
In this paper a seventeen year old question by Porter is answered showing that the Banaschewski-Fomin-Šanin extension μX of a space X can be embedded in the upper Stone-Čech compactification, β + X. Frolik and Liu characterized H-closed spaces as maximal Hausdorff subspaces in their closure in Π C+( X) I +; that is, X is H-closed iff e[ X] is a maximal Hausdorff subspace of β + X. This result is strengthened/generalized by showing that σX, μX and, in fact, every strict H-closed extension of X can be embedded in β + X. However, there may be infinitely many copies of every strict H-closed extension within β + X.
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