*Definition [#wdbd9c9f]
A regular Hausdorff space X is preorthocompact iff for each open cover C of X, there is a reflexive relation V on X such that for each x in X, V(x) is open and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V%5ccirc%20V%28x%29$%7d%25.png); is a subset of some member of C.

*Reference [#m78943c0]
-Hans-Peter Kunzi and Peter Fletcher, ''Some Questions Related to Almost 2-Fully Normal Spaces'', Rocky Mountain J. Math. Vol.15 (Nov. 1985).