strongly compact
*Definition [#he6d302a]
A topological space is called strongly compact iff every [[preopen]] cover has a finite subcover.

*Property [#j1e82401]
-[Ganster1987] For a topological space X, the following are equivalent
++X is strongly compact
++X is compact and every infinite subset of X has a nonempty interior.
++X is [[quasi H-closed]] and every infinite subset of X has a nonempty interior.
-[Ganster1987] The 1?point?compactification of any discrete space is strongly compact.

*Reference [#o339976a]
-J. Dontchev, M. Ganster and T. Noiri, ''On p-closed spaces'', Internat. J. Math. & Math. Sci. Vol.24, No.3 (2000) pp.203-212.
-M. Ganster, ''Some remarks on strongly compact spaces and semi compact spaces'', Bull. Malaysian Math. Soc. (10) 2 (1987) pp.67-81.