The “ Way - Below ” Relation

In the paper the “way-below” relation, in symbols x y, is introduced. Some authors prefer the term “relatively compact” or “way inside”, since in the poset of open sets of a topology it is natural to read U V as “U is relatively compact in V ”. A compact element of a poset (or an element isolated from below) is defined to be way below itself. So, the compactness in the poset of open sets of a topology is equivalent to the compactness in that topology. The article includes definitions, facts and examples 1.1–1.8 presented in [11, pp. 38–42].