We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

If a sequence of random closed sets Xn in a separable complete metric space converges in distribution in the Wijsman topology to X, then the corresponding sequence of cores (sets of probability measures dominated by the capacity functional of Xn) converges to the core of the capacity of X. Core convergence is achieved not only in the Wijsman topology, but even in the stronger Vietoris topology....

Dedicated to R. T. Rockafellar on his 60th Birthday In a Banach space X, we introduce a criterion for comparing the Wijsman topologies that are induced by two equivalent norms of X on the hyperspace of closed convex sets C(X). Thereafter, we study the duality map associated with the unit ball of a given norm of X in relation to its composition with the polarity map. This more geometrical descri...

In this paper, we show that for an almost locally separable metrizable space X, if its Wijsman hyperspace induced by one compatible metric is Baire, then X itself must be Baire. We also provide an example to demonstrate the necessity of separability.

In this article we introduce different types of regularity for multisubmeasures with respect to the Wijsman topology and establish several relationships with the types of regularity that we have studied in [3] and [5] with respect to the Hausdorff, respectively, the Vietoris topology. AMS Mathematics Subject Classification (2000): 28C15, 49J53

The main object of this paper is to introduce and study a new concept of f-Wijsman lacunary statistical convergence of sequences of sets, where f is an unbounded modulus. The definition of Wijsman lacunary strong convergence of sequences of sets is extended to a definition of Wijsman lacunary strong convergence with respect to a modulus for sequences of sets and it is shown that, under certain ...