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The Scientific World Journal
Volume 2014, Article ID 640323, 5 pages
http://dx.doi.org/10.1155/2014/640323
Research Article

Topologies on Superspaces of TVS-Cone Metric Spaces

Xun Ge1 and Shou Lin2,3

1School of Mathematical Sciences, Soochow University, Suzhou 215006, China
2Department of Mathematics, Ningde Normal University, Fujian 352100, China
3Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, China

Received 6 August 2013; Accepted 31 October 2013; Published 22 January 2014

Academic Editors: R. Abu-Saris, P. Bracken, S. Jafari, and B. Nagy

Copyright © 2014 Xun Ge and Shou Lin. 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.

Abstract

This paper investigates superspaces and of a tvs-cone metric space , where and are the space consisting of nonempty subsets of and the space consisting of nonempty compact subsets of , 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 and , which makes it possible to generalize some results of superspaces from metric spaces to tvs-cone metric spaces.