Definition
A subset A of a topological space X is called relatively realcompact in X iff , where νX denotes the Hewitt realcompactification of X.
Remark
- Recall that A is relatively compact? in X iff is compact, and that A is relatively pseudocompact in X iff .
- Note that if A is relatively realcompact in X, the closure of A in X is realcompact space. However, the converse is not true.
Reference
- J. J. Shommer, Relatively realcompact sets and nearly pseudocompact spaces, Comment. Math. Univ. Calorin. 34,2 (1993) 375-382.