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Given a Hausdorff space X, we calculate the tightness and the character of the hyperspace CL (X) of X, endowed with either the co-compact or the lower Vietoris topology, and give some estimates for the tightness of CL (X), endowed with the Fell topology.Some properties related to first-countability and countable tightness, such as sequentiality, Frechet property and, less directly,...
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