Abstract:We calculate the density of the hyperspace of a metric space, endowed with the Hausdorff or the locally finite topology. To this end, we introduce suitable generalizations of the notions of totally bounded and compact metric space.
Keywords: hyperspace, density, metric and metrizable space, Hausdorff metric hypertopology, locally finite hypertopology, GTB space, GK space
AMS Subject Classification: Primary 54B20; Secondary 54A25, 54E35