strongly relatively pseudocompact

Definition

A subset A of a topological space X is called strongly pseudocompact in X iff for every cozero set neighborhood P of A, every continuous function on P is bounded on A.

Reference

Mary Anne Swardson and Paul J. Szeptycki, When X^* is a P' space, Canad. Math. Bull. Vol. 39 (4), 1996 pp. 476-485.