Realcompact Alexandroff frames

This paper complements an earlier one by the authors which showed, among other things, that every completely regular σ-frame is complete in the natural uniformity associated with its continuous real-valued functions — very much a characteristic property associated with realcompactness. It is natural then, when exploiting the pointfree setting for realcompactness, to rather work with Alexandroff frames, which we show here are sufficiently close to completely regular frames to maintain the distinctions between the different notions of realcompactness found there, but nevertheless still retain desirable properties analogous to those that their classical archetypes the Alexandroff spaces have in contrast to their topological counterparts.