*Definition [#z257752c]
A topological space X is called pointwise star-orthocompact if for every open cover &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bU%7d$%7d%25.png); of
X, there exists an open Q-collection &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bV%7d=%5c%7bV_x:x%5cin%20X%5c%7d$%7d%25.png); such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$x%5cin%20V_x%5csubset%20%5cmathrm%7bSt%7d%28x%2c%5cmathcal%7bU%7d%29$%7d%25.png);.
Here, a collection U of open subsets is called Q-collection if for every subcollection V of U, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5ccap%5cmathcal%7bV%7d$%7d%25.png); is open.

*Reference [#uf23a52f]
-Gary Gruenhage, ''On closed images of orthocompact spaces'', Proc. Amer. Math. Soc. Vol.77, No.3, pp.389-394 (1979)