Hereditary normality-type properties of hyperspaces (Q2268624)

Let \(X\) be a Hausdorff topological space and \(\exp(X)\) the space of all (nonempty) closed subsets of \(X\) endowed with the Vietoris topology. The author studies \(D\)-normality of \(\exp(X)\). The property of \(D\)-normality goes back to H. Brandenburg and is implied by normality and holds in perfect developable spaces. The main theorem of the paper is a common extension of a result of Choban and of another result by the author. The theorem states that if \(\exp(X)\) is hereditary \(D\)-normal then \(X\) is a metrizable compact space.