almost preorthocompact

Definition

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 and x is in V(z), {x, y} is a subset of some member of C.

Property

• Every almost preorthocompact space is point-star preorthocompact.

Reference

• Hans-Peter Kunzi and Peter Fletcher, Some Questions Related to Almost 2-Fully Normal Spaces, Rocky Mountain J. Math. Vol.15 (Nov. 1985).