Normality and countable paracompactness of hyperspaces of ordinals (Q864449)

For a space \(X\), \(2^X\) denotes the space consisting of all nonempty closed subsets of \(X\) with the Vietoris topology and \({\mathcal K}(X)\) denotes the subspace of \(2^X\) consisting of all compact subsets of \(X\). The author discusses normality and countable paracompactness of hyperspaces of ordinals and proves the following results: Theorem 5. \({\mathcal K}(\alpha)\) is countably paracompact for all nonzero-ordinals \(\alpha\). Theorem 8. If \(\kappa\) is a regular uncountable cardinal, then \({\mathcal K}(\kappa)\) is normal. The author also discusses the space \(2^X\).