The concept of an H-set (a
generalization of an H-closed space) was introduced by N. V. Velicko. In
this paper we obtain internal properties of H-sets in terms of the Iliadis
absolute EX and the Hausdorff absolute PX. Some of the main results
are:
An H-closed space X is Urysohn iff P−1(A) is an H-set in PX for every
H-set A ⊂ X.
If A is an H-closed subset of X then there exists a compact B ⊂ EX such
that π(B) = A and π : B → A is 𝜃-continuous.
There exists a space X and an H-set A ⊂ X which is not the image of a
compact subset of EX.
If {Hi}i is a chain of H-closed subspaces in X, then ⋂Hi is the image of
a compact subset of EX.
A question of A. Dow and J. Porter is answered and a question of R. G. Woods is
answered partially.
