Resumen de Local compactness of the hyperspace CLC(X)

Robbie A. Beane

• We provide a necessary condition and a sufficient condition for local compactness of CLC(X), the hyperspace of closed connected subsets of a metric space X, as well as a sufficient condition for metrizability of CLC(X). To simplify the statement of these conditions we introduce the terms buffer and totally buffered . Some basic theory relating to these new concepts is developed.