Definition
A space is called weakly pseudocompact iff there exists some compact space bX such that X is embedded as a G_δ dense subset in bX (which means that every nonempty G_δ-set in bX meets X).
Reference
F. W. Eckertson, Sums, products, and mappings of weakly pseudocompact spaces, Topology and its Aplications 72 (1996) 149-157.