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- Author or Editor: Daniel Jardón x
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Abstract
A space X is called ultracomplete if it has countable character in its Stone–Čech compactification βX. A space X is called almost locally compact if the set of all points at which X is not locally compact is contained in a compact set of countable outer character. For a given Tychonoff space X let 2 X be the hyperspace of all nonempty compact subsets of X endowed with the Vietoris topology. We prove that 2 X is almost locally compact if and only if X is locally compact. We also prove that for a countably compact ultracomplete space X the hyperspace F n (X)={K∊2 X ∣K has at most n points} is also countably compact ultracomplete for every natural number n. We also analyse ultracompleteness of F n (X) and 2 X .
