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

n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{p}_{0}(x)$-valued set multifunctions ($x$ being a linear,topological space), in order to obtain egoroff and lusin type theorems forset multifunctions in the vietoris hypertopology. some mathematicalapplications are established and several physical implications of thema...

Here a typical topological semigroup C(G) is studied. A partial equivalence [1] is defined on C(G) compatible with its semigroup structure. Also a uniformity is constructed giving the Vietoris topology [3] on C(G).

An estimate for the Novak number of a hyperspace with the Vietoris topology is given. As a consequence it is shown that this cardinal function can decrease passing from a space to its hyperspace.

In algebraic topology it is well-known that, using the Mayer-Vietoris sequence, the homology of a space X can be studied splitting X into subspaces A and B and computing the homology of A, B, A∩B. A natural question is to which an extent persistent homology benefits of a similar property. In this paper we show that persistent homology has a Mayer-Vietoris sequence that in general is not exact b...

The purpose of this article is to propose a unified theory for topologies on the closed subsets of a metrizable space. It can be shown that all of the standard hyperspace topologies—including the Hausdorff metric topology, the Vietoris topology, the Attouch-Wets topology, the Fell topology, the locally finite topology, and the topology of Mosco convergence—arise as weak topologies generated by ...

This paper investigates superspaces 𝒫0(X) and 𝒦0(X) of a tvs-cone metric space (X, d), where 𝒫0(X) and 𝒦0(X) are the space consisting of nonempty subsets of X and the space consisting of nonempty compact subsets of X, respectively. The purpose of this paper is to establish some relationships between the lower topology and the lower tvs-cone hemimetric topology (resp., the upper topology and the...