Displaying similar documents to “Polishness of weak topologies generated by gap and excess functionals.”

Relative Compactness for Hyperspaces

Sianesi, Francesca (1999)

Serdica Mathematical Journal

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The present paper contains results characterizing relatively compact subsets of the space of the closed subsets of a metrizable space, equipped with various hypertopologies. We investigate the hyperspace topologies that admit a representation as weak topologies generated by families of gap functionals defined on closed sets, as well as hit-and-miss topologies and proximal-hit and-miss topologies.

Coincidence of Vietoris and Wijsman Topologies: A New Proof

Holá, L’. (1997)

Serdica Mathematical Journal

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Let (X, d) be a metric space and CL(X) the family of all nonempty closed subsets of X. We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric d forces X to be a compact space. In the literature only a more involved and indirect proof using the proximal topology is known. Here we do not need this intermediate step. Moreover we prove that (X, d) is boundedly compact if and only if the bounded Vietoris and Wijsman topologies...