Last-modified: 2010-12-28 (火) 21:13:24
A space X is said to be a-realcompact if every maximal open cover has a countable subcover.
- 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.
Nancy Dykes, Generalizations of Realcompact Spaces, Pacific Journal of Mathematics Vol. 33, No. 3, 1970.