Title: ON <i>H</i>-Sets and Open Filter Adherences<sup>(1)</sup>
Abstract: Abstract The relationship between H -sets and open filter adhérences is considered. The open filter adhérences of an H -closed space are shown to be H -sets; and, a necessary and sufficient condition is given for an H -set S, of a Hausdorff space X, to be an open filter adherence. A necessary condition is determined for the existence of a minimal adherent set which contains S; and, in the case that X is H -closed, sufficient conditions are determined. As a related result, an H -closed space X is shown to be seminormal if every H -set of X possesses a neighborhood base consisting of regular open sets.