COMPACTIFICATION AND LOCAL CONNECTEDNESS OF FRAMES

A classical result in the theory of Tychonoff spaces is that, for any such space X, its Stone-Cech compactification beta-X is locally connected iff X is locally connected and pseudocompact. Since all concepts involved in this generalize from spaces to frames, it is natural to ask whether this result already holds for the latter, and the main purpose of this paper is to show this is indeed the case (Proposition 2.3). Further, for normal regular frames, we obtain the frame counterpart of an analogous result of Wallace in terms of a certain property of covers (Proposition 3.5). Finally, we establish a number of additional results concerning connectedness which seem to be of independent interest.