A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the ...

Comfort and Hager investigate the notion of a maximal realcompact space and ask about the relationship to the first measurable cardinal m. A space is said to be a P (m) space if the intersection of fewer than m open sets is again open. They ask if each realcompact P (m) space is maximal realcompact. We establish that this question is undecidable.

Two classes of spaces are studied, namely locally realcompact spaces and HNcomplete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences ...

We provide a fairly general method, which is straightforward and widely applicable, for constructing some coreflections in the category of nearness frames. The method captures all coreflective subcategories with 1 1 coreflection maps; this includes the well-known uniform, totally bounded and separable coreflections. The primary application of this method answers in the affirmative the question ...