*Definition [#e6fdfe86]
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 [#n91aba43]
cf. [[realcompact]].

*Reference [#h6aee1a5]
John J. Schommer and Mary Anne Swardson, ''Almost* realcompactness'', Commentationes Mathematicae Universitatis Carolinae, Vol.42 (2001), No.2, 383-392.