On a generalization of pointfree realcompactness (Q392559)

Almost* realcompactness for topological spaces (a generalization of realcompactness defined in terms of ultrafilters of cozero sets) was introduced in [\textit{J. J. Schommer} and \textit{M. A. Swardson}, Commentat. Math. Univ. Carol. 42, No. 2, 385--394 (2001; Zbl 1053.54032)]. In the article under review, the authors introduce a conservative extension of almost* realcompactness to a pointfree setting (i.e. a topological space is almost* realcompact iff its topology is an almost* realcompact frame). An ultrafilter characterization of realcompact frames is given and the latter are shown to be almost* realcompact. Preservation of almost* realcompactness under frame homomorphisms is studied too.