Topologies on Superspaces of TVS-Cone Metric Spaces

This paper investigates superspaces 𝒫 (0)(X) and 𝒦 (0)(X) of a tvs-cone metric space (X, d), where 𝒫 (0)(X) and 𝒦 (0)(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 upper tvs-cone hemimetric topology to the Vietoris topology and the Hausdorff tvs-cone hemimetric topology) on 𝒫 (0)(X) and 𝒦 (0)(X), which makes it possible to generalize some results of superspaces from metric spaces to tvs-cone metric spaces.