EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 98(112), pp. 271–279 (2015)

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On the metrizability of TVS-cone metric spaces

Shou Lin, Kedian Li, Ying Ge

Department of Mathematics, Ningde Normal University, Ningde, P. R. China; Department of Mathematics, Zhangzhou Normal University, Zhangzhou, P. R. China; School of Mathematical Sciences, Soochow University, Suzhou, P. R. China

Abstract: Metric spaces are cone metric spaces, and cone metric spaces are TVS-cone metric spaces. We prove that TVS-cone metric spaces are paracompact. A metrization theorem of TVS-cone metric spaces is obtained by a purely topological tools. We obtaine that a homeomorphism $f$ of a compact space is expansive if and only if $f$ is TVS-cone expansive. In the end, for a TVS-cone metric topology, a concrete metric generating the topology is constructed.

Keywords: Stone's method; TVS-cone metric space; paracompact; metrizable; TVS-cone expansive homeomorphism

Classification (MSC2000): 54D20;54E35;46A19; 54E99;54H20

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Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.

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