Topologies on Superspaces of TVS-Cone Metric Spaces
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/640323 |
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| author | Xun Ge Shou Lin |
| author_facet | Xun Ge Shou Lin |
| author_sort | Xun Ge |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-edba2839e38b4d1788bd489073d2de06 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-edba2839e38b4d1788bd489073d2de062025-02-03T05:48:04ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/640323640323Topologies on Superspaces of TVS-Cone Metric SpacesXun Ge0Shou Lin1School of Mathematical Sciences, Soochow University, Suzhou 215006, ChinaDepartment of Mathematics, Ningde Normal University, Fujian 352100, ChinaThis 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.http://dx.doi.org/10.1155/2014/640323 |
| spellingShingle | Xun Ge Shou Lin Topologies on Superspaces of TVS-Cone Metric Spaces The Scientific World Journal |
| title | Topologies on Superspaces of TVS-Cone Metric Spaces |
| title_full | Topologies on Superspaces of TVS-Cone Metric Spaces |
| title_fullStr | Topologies on Superspaces of TVS-Cone Metric Spaces |
| title_full_unstemmed | Topologies on Superspaces of TVS-Cone Metric Spaces |
| title_short | Topologies on Superspaces of TVS-Cone Metric Spaces |
| title_sort | topologies on superspaces of tvs cone metric spaces |
| url | http://dx.doi.org/10.1155/2014/640323 |
| work_keys_str_mv | AT xunge topologiesonsuperspacesoftvsconemetricspaces AT shoulin topologiesonsuperspacesoftvsconemetricspaces |