Definition
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 is a subset of some member of C.
Reference
- Hans-Peter Kunzi and Peter Fletcher, Some Questions Related to Almost 2-Fully Normal Spaces, Rocky Mountain J. Math. Vol.15 (Nov. 1985).