R. M. Stephenson, Jr.
(Trans. Amer. Math. Soc. 133 (1968), 537-546) has established the existence
of a completely Hausdorff-closed extension Xγ of an arbitrary completely
Hausdorff space X. Stephenson demonstrates that X′ enjoys many interesting
properties of the Stone −Č ech compactification. This paper shows that, by a
modification of the topology, X′ is made also to possess a property which is in the
line of the celebrated property of the Stone-Cechv compactification of a
completely regular Hausdorff space that it is the largest amongst all Hausdorff
compactifications.
