ψ-compact

Definition

Let X be a Tychonoff space.
Let C_K(X) denote the collection of continuous functions with compact support, C_Ψ(X) the collection of continuous functions with pseudocompact support.
X is called Ψ-compact if C_K(X)=C_Ψ(X).

Remark

cf. realcompact.

Reference

John J. Schommer and Mary Anne Swardson, Almost* realcompactness, Commentationes Mathematicae Universitatis Carolinae, Vol.42 (2001), No.2, 383-392.