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Normal Vietoris implies compactness: a short proof

G. Di MaioE. MeccarielloSomashekhar Naimpally — 2004

Czechoslovak Mathematical Journal

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.

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