*Definition 1 [#k38c4aed]
-A topological space X is co-compact if any [[co-open]] cover of X has a finite subcover.

*Definition 2 [#tb39e6ae]
A topological space X is said to be co-compact if there is a collection D of a closed subsets which satisfies the following:
+any subcollection of D with [[fip]] has nonempty intersection;
+if U is an open subset of X and if x is a point in U, then there is some V in D with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$x%5cin%5cmathrm%7bInt%7d%28V%29%5csubset%20V%5csubset%20U$%7d%25.png);.
*Reference [#k069ddbf]
: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|
--H. Bennett and D. J. Lutzer, ''Strong completeness properties in topology'', Questions and Answers in General Topology, 27(2009), 107-124.
--http://www.math.wm.edu/~lutzer/drafts/BigBushes.pdf (preprint)