We give a construction of Wallman-type realcompactifications of a frame $L$ by considering regular sub $\sigma$-frames the join of which generates $L$. In particular, we show that the largest such regular sub $\sigma$-frame gives rise to the universal realcompactification of $L$.

In this paper, we clarify the relationship among the Vietoris-type homology theories and the microsimplicial homology theories, where the latter are nonstandard homology theories defined by M.C. McCord (for topological spaces), T. Korppi (for completely regular topological spaces) and the author (for uniform spaces). We show that McCord’s and our homology are isomorphic for all compact uniform spaces and that Korppi’s and our homology are isomorphic for all fine uniform spaces. Our homology shares...