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 relations...

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Detalles Bibliográficos
Autores principales: Ge, Xun, Lin, Shou
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3919050/
https://www.ncbi.nlm.nih.gov/pubmed/24587739
http://dx.doi.org/10.1155/2014/640323
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author Ge, Xun
Lin, Shou
author_facet Ge, Xun
Lin, Shou
author_sort Ge, Xun
collection PubMed
description 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.
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spelling pubmed-39190502014-03-02 Topologies on Superspaces of TVS-Cone Metric Spaces Ge, Xun Lin, Shou ScientificWorldJournal Research Article 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. Hindawi Publishing Corporation 2014-01-22 /pmc/articles/PMC3919050/ /pubmed/24587739 http://dx.doi.org/10.1155/2014/640323 Text en Copyright © 2014 X. Ge and S. Lin. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Ge, Xun
Lin, Shou
Topologies on Superspaces of TVS-Cone Metric Spaces
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
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3919050/
https://www.ncbi.nlm.nih.gov/pubmed/24587739
http://dx.doi.org/10.1155/2014/640323
work_keys_str_mv AT gexun topologiesonsuperspacesoftvsconemetricspaces
AT linshou topologiesonsuperspacesoftvsconemetricspaces

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