*Definition [#ob5002fd]
A space X is said to be a-realcompact if every [[maximal]] open cover has a countable subcover.

*Property [#rab345c6]
-Suppose there exist a [[perfect]] mapping from X onto Y. X is a-realcompact iff. Y is a-realcompact.
-Every regular [[realcompact]] space is a-realcompact.
-A Tychonoff space is a-realcompact iff every ultrafilter of closed sets with [[cip]] is fixed.

*Reference [#x117da09]
Nancy Dykes, ''Generalizations of Realcompact Spaces'', Pacific Journal of Mathematics Vol. 33, No. 3, 1970.