Topologies on Superspaces of TVS-Cone Metric Spaces. (22nd January 2014)

• Record Type: Journal Article
• Authors: Ge, Xun; Lin, Shou
• Other Names: Abu-Saris R. Academic Editor.; Bracken P. Academic Editor.; Jafari S. Academic Editor.; Nagy B. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-01-22
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/640323
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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.