*Definition 1 [#k1d791db]
A topological space is called semicompact if every [[semiopen]] cover has a finite subcover.

*Definition 2 [#q550deec]
Same as [[locally peripherally compact]].

*Property [#yc742dac]
The following properties are all for Definition 1.
-[Dorsett1981] A space is semicompact iff it satisfies the following.
++For every infinite subset S, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathrm%7bint%7d%28%5cmathrm%7bcl%7d%28S%29%29%5cneq%20%5cemptyset$%7d%25.png);.
++Every disjoint family of nonempty open sets is finite.
-[Ganster1987] A space X is semicompact iff it satisfies the following.
++X is [[S-closed]].
++For every infinite subset S, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathrm%7bint%7d%28%5cmathrm%7bcl%7d%28S%29%29%5cneq%20%5cemptyset$%7d%25.png);.

*Reference [#dfcc16ea]
:Definition 1|
--Dorsett, Ch. ''Semi-compact R1 and product spaces'', Bull. Malaysian Math. Soc., 3(2) (1980), 15-19.
--Ch. Dorsett, Semi compactness, semi separation axioms, and product spaces, Bull. Malaysian Math. Soc. (2) 4 (1981), 21-28.
--M. Ganster, ''Some remarks on strongly compact spaces and semi compact spaces'', Bull. Malaysian Math. Soc. (10) 2 (1987), 67-81.
:Definition 2|
K. Morita, ''On closed mappings. II'', Proc. Japan Acad. Vol.33, No.6 (1957) pp.325-327