In a sense, this paper is a sequel to BANASCHEWSKI [l], dealing with aspects of compactification and frames that have come to the fore during the 21 years since [l] was written. A t that time, the concern was to describe the construction of compact &us-DORFF extension spaces for a given space in terms of frames, specifically as filter spaces in frames. The object of this was to explicate the lattice theoretic essence of certain familiar constructions in topology, much in the spirit of other work on frames a t the time, such as DOWKER-PAPERT [6] which I had heard presented a t the 1966 Prague Topological Symposium. In the years since then, frames have acquired an important new feature, as the constructive aspect of topological spaces (JOHNSTONE 191). I n this spirit, compactification of frames as such becomes a topic of interest, as opposed t o merely using a frame setting for describing compactification of spaces as in [ 11. Work in this latter vein is not new: thus, BAXASCHEWSKI-MULVEY [3] establieh the STONE-CECH compactification of frames, and JOHNSTONE [8] presents an alternative construction of this. Thc aim of the present note, then, is to provide a comprehensive view of all compactifications of a given frame. Considering some aspects of the STONE-CECII compactification of frames, it does not come as a surprise that this can be achieved with a tool which originated in the study of compactification of spaces, going back to FREUDE~TTIIAL [ 71. This paper was written during sabbatical leave spent a t the University of Cape Town. Financial assistcncc from that institution as well as from the Natural Sciences and Engineering Research Council of Canada are gratefully acknowledged.
JOHNSTONE [ 91.
We begin by recalling some background. For general information on frames, see