Normality and countable paracompactness of hyperspaces of ordinals

For an ordinal α, α2 denotes the collection of all nonempty closed sets of α with the Vietoris topology and K(α) denotes the collection of all nonempty compact sets of α with the subspace topology of α2. It is well known that α2 is normal iff cfα=1. In this paper, we will prove that for every nonzero-ordinal α:(1)α2 is countably paracompact iff cfα≠ω.(2)K(α) is countably paracompact.(3)K(α) is normal iff, if cfα is uncountable, then cfα=α. In (3), we use elementary submodel techniques.