Definition
A topological space is said to be super countably paracompact iff. for every decreasing sequence of closed sets
with an empty intersection, there is a decreasing sequence of cozero sets
with
and
have an empty intersection.
Reference
John J. Schommer and Mary Anne Swardson, Almost realcompactness, Commentationes Mathematicae Universitatis Carolinae, Vol. 42 (2001), No. 2, 383–392.