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Last-modified: 2010-12-28 (火) 21:13:24

Definition Edit

A space X is said to be a-realcompact if every maximal open cover has a countable subcover.

Property Edit

  • 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 Edit

Nancy Dykes, Generalizations of Realcompact Spaces, Pacific Journal of Mathematics Vol. 33, No. 3, 1970.