Definition
A space (X,T) is called countably rc-compact if every countable cover of X by regular closed subsets has a finite subcover for X.
Remark
- It is called countably S-closed, too.
Reference
Bassam Al-Nashef, Countalby I-compact spaces, International Journal of Mathematics and Mathematical Sciences, Volume 26 (2001), Issue 12, Pages 745-751.