Abstract

ut by applying T to some poset (namely the original poset less the bottom). Both these properties fail to hold constructively, if the lift monad is interpreted as "adding a bottom"; see Remark below. If, on the other hand, we interpret the lift monad as the one which freely provides supremum for each subset with at most one element (which is what we shall do), then the first property holds; and we give a necessary and sufficient condition that the second does. Finally, we shall investigate the lift monad in the context of (constructive) locale theory. I would like to thank Bart Jacobs for guiding me to the litterature on Z-systems; to Gonzalo Reyes for calling my attention to Barr's work on totally connected spaces; to Steve Vickers for some pertinent correspondence. I would like to thank the Netherlands Science Organization (NWO) for supporting my visit to Utrecht, where a part of the present research was carried out, and for various travel support from

Citations