title: Topologies on superspaces of TVS-cone metric spaces.
abstract: 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 upper tvs-cone hemimetric topology to the Vietoris topology and the Hausdorff tvs-cone hemimetric topology) on 𝒫0(X) and 𝒦0(X), which makes it possible to generalize some results of superspaces from metric spaces to tvs-cone metric spaces.
authors.affiliation: School of Mathematical Sciences, Soochow University, Suzhou 215006, China.
authors.forename: Xun
authors.initials: X
authors.lastname: Ge
authors.affiliation: Department of Mathematics, Ningde Normal University, Fujian 352100, China ; Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, China.
authors.forename: Shou
authors.initials: S
authors.lastname: Lin
mesh_terms: D055641:Mathematical Concepts