*Definition 1[#y899f631]
-A subset A of a space X is an H-set in X if for each open cover C of A, there is a finite subfamily F of C such that the closures of members of F cover A.

*Definition 2? [#y6f2c89a]
-A nonempty subset S of a space X is an H-set (of X ) if every open filter on X which meets S, has a cluster point in S.

*Reference [#fe5af22e]
:Definiton 1| R.F. Dickman, Jr. and J.R. Porter, ''Between minimal Hausdorff and compact Hausdorff spaces'', Topology Proc. Vol.9 (1984), p.243-268.

:Definition 2| Krystock, Robert L., ''Adherent compact spaces. (English)'', Proc. Am. Math. Soc. 107, No.4, 1117-1125 (1989).