Embeddings in the upper Stone-Čech compactification

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 ΠC+(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.