Call a topological space "(* )", if each of its closed, pseudo-compact subsets is countably compact.
Does anyone know of a name for (* ), which appeared in the literature?
Since I'm just looking for any reference, I omit to give precise definitions. Whether this name has been used in the T2 / Tychonoff context only or not, also doesn't matter.
Of course, normal, T2 spaces are (* ). Moreover, a space is countably compact, iff it is pseudocompact and (* ). This gives a lot of examples, which are not (* ).
A related, widely used notation is isocompactness (= closed, countably compact subsets are compact). Obviosuly, a space is isocompact and (* ), iff each of its closed, pseudocompact subsets is compact. Hence, a name for this property might also be helpful.
Update
Just after posting this question, I noticed that "strong isocompactness" in this paper is similar to the second property, see Prop. 3.0. However, they are not identical, since "relatively pseudocompact" in this paper differs from "pseudocompact".