THE WALLMAN COMPACTIFICATION OF FRAMES

Abstract

We show that a B-conjunctive frame L, where B is a normal base for L gives rise to a strong inclusion on L and therefore a compactification of L. The resulting compact regular frame corresponds to the quotient frame obtained by Johnstone in his construction of the Wallman compactification for frames. It is also shown that, in the presence of pseudocompactness the Wallman compactification and the Wallman realcompactification coincide.