On Regularity via h-Open Sets

We investigate regularity properties defined by means of h-open sets, with systematic use of the associated topology τh=hO(X). In this framework, h-regularity separates points from τ-closed sets by τh-open sets, whereas strong h-regularity is precisely ordinary regularity of (X,τh). After recalling the established characterization of h-regularity, we obtain preservation results under suitable mappings, study the relation with h∗-regularity and extremal h-disconnectedness, analyze strong (h,θ)-continuity, and establish hereditary results for the regularity notions under the appropriate subspace hypotheses. We also connect the h-R0 condition with the associated topology and with strong h-regularity.