CONSTRUCTIVE POINTS OF POWERLOCALES

Results of Bunge and Funk and of Johnstone, providing constructively s ound descriptions of the global points of the lower and upper powerloc ales, are extended here to describe the generalized points and proved in a way that displays in a symmetric fashion two complementary treatm ents of frames: as suplattices and as preframes. Also described here a re the points of the Vietoris powerlocale. In each of two special case s; an exponential $(D) ($ being the Sierpinski locale) is shown to be homeomorphic to a powerlocale: to the lower powerlocale when D is disc rete, and to the upper powerlocale when D is compact regular.