Given a metric space X we characterize those Y so that the realcompactification of X×Y is just the product of X with the realcompactification of Y . Examples are constructed to illustrate that the properties involved do depend on the metric spaces

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 ...

for each a ∈ A. We denote the top and bottom elements of a σ-frame A respectively by 1A and 0A. σ-Frame homomorphisms preserve countable joins and finite meets. The resulting category is denoted σFrm. Extending the above notions by allowing arbitrary subsets and arbitrary joins in the definitions leads to the notions of a frame and a frame homomorphism, and the corresponding category Frm of fra...

The present paper indicate a method of obtaining the Hewitt realcompactification vX of a Tychonoff space X, by considering a distinguished family of maximal regular congruences, viz., those which are real, on the hemiring C+(X) of all the non-negative real valued continuous functions on X.