*Definition [#ld57bae5]
A space X is called almost preorthocompact provided that, if C is a open cover of X, there is a reflexive relation V on X so that, for each z in X, V(z) is open and whenever y is in &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V%5ccirc%20V%28x%29$%7d%25.png); and x is in V(z), {x, y} is a subset of some member of C.

*Property [#eacbdac7]
-Every almost preorthocompact space is [[point-star preorthocompact]].

*Reference [#m7df536f]
-Hans-Peter Kunzi and Peter Fletcher, ''Some Questions Related to Almost 2-Fully Normal Spaces'', Rocky Mountain J. Math. Vol.15 (Nov. 1985).