Topologies on Superspaces of TVS-Cone Metric Spaces

Abstract EN

This paper investigates superspaces ? 0 ( X ) and ? 0 ( X ) of a tvs-cone metric space ( X , d ) , where ? 0 ( X ) and ? 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 ? 0 ( X ) and ? 0 ( X ) , which makes it possible to generalize some results of superspaces from metric spaces to tvs-cone metric spaces.