*Definition [#k6de563e]
-A space X is &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c!_%7b1%5cfrac%7b1%7d%7b2%7d%7d%20%5c%5d%7d%25.png);-starcompact if for every open cover U of X, there exists a finite subfamily V of U such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cdisplaystyle%20St%28%5ccup%5cmathcal%7bV%7d%2c%5cmathcal%7bU%7d%29=X%20%5c%5d%7d%25.png);, where &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cdisplaystyle%20St%28%5ccup%5cmathcal%7bV%7d%2c%5cmathcal%7bU%7d%29=%5cbigcup%5c%7bU%5cin%5cmathcal%7bU%7d%7c%20U%5ccap%28%5ccup%5cmathcal%7bV%7d%29%5cneq%5cemptyset%5c%7d%20%5c%5d%7d%25.png);

*Remark [#pe30d0bc]
-&ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c!_%7b1%5cfrac%7b1%7d%7b2%7d%7d%20%5c%5d%7d%25.png);-starcompact space is called [[starcompact]].
-&ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c!_%7b1%5cfrac%7b1%7d%7b2%7d%7d%20%5c%5d%7d%25.png);-starcompact space is called [[1-starcompact]].
*Reference [#o1b5c026]
-Song, Yan-Kui(PRC-NJN-IMM),''Remarks on K-starcompact spaces. (English summary)'',commun. Korean Math. Soc. 22 (2007), no. 4, 569--573.