*Definition [#e0108d81]
A topological space X is called point-star metacompact provided that, if C is an open cover of X, there is a [[point-finite]] open refinement R of &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bC%7d%5e*$%7d%25.png); so that, for each x in X, there exists U_x in R so that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$x%5cin%20U_x%5csubset%20%5cmathrm%7bSt%7d%28x%2c%5cmathcal%7bC%7d%29$%7d%25.png);. Here &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bC%7d%5e*=%5c%7b%5cmathrm%7bSt%7d%28x%2c%5cmathcal%7bC%7d%29:x%5cin%20X%5c%7d$%7d%25.png);.

*Reference [#n8b89327]
-Hans-Peter Kunzi and Peter Fletcher, ''Some Questions Related to Almost 2-Fully Normal Spaces'', Rocky Mountain J. Math. Vol.15 (Nov. 1985).