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co-compact

Last-modified: 2015-11-17 (火) 19:20:09

Definition 1 Edit

  • A topological space X is co-compact if any co-open cover of X has a finite subcover.

Definition 2 Edit

A topological space X is said to be co-compact if there is a collection D of a closed subsets which satisfies the following:

  1. any subcollection of D with fip has nonempty intersection;
  2. if U is an open subset of X and if x is a point in U, then there is some V in D with imgtex.fcgi?%5bres=100%5d%7b$x%5cin%5cmathrm%7bInt%7d%28V%29%5csubset%20V%5csubset%20U$%7d%25.png.

Reference Edit

Definition 1
  • Abd El-Monsef, M. E.(ET-TANT) and Kozae, A. M.(ET-TANT),Remarks on $s$-closed spaces (Arabic summary), Qatar Univ. Sci. Bull. 6 (1986), 11--21.
Definition 2