*Definition [#l3abcb8c]
-A space X is countably starcompact if for every countable open cover U of X , there exists a finite subset B of X such that  &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20St%28B%2c%5cmathcal%7bU%7d%29=X%20%5c%5d%7d%25.png);.

*Remark [#f01265d3]
-See [[starcompact]] for notation.

*Reference [#zdaae3ec]
-Song, Yan-Kui(J-SHIZS), ''Countable star-covering properties. (English summary) Research in general and geometric topology (Japanese) (Kyoto, 1999)'', Sūrikaisekikenkyūsho Kōkyūroku No. 1126 (2000), 79--87.