Normality and countable paracompactness of hyperspaces of ordinals

For an ordinal α, 2 α 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 2 α . It is well known that 2 α is normal iff cf α = 1 . In this paper, we will prove that for every nonzero-ordinal α:(1) s countably paracompact iff cf α ≠ ω . ) is countably paracompact. ) is normal iff, if cfα is uncountable, then cf α = α . ), we use elementary submodel techniques.