Geodesic
On the Metrizability of TVS-Cone Metric Spaces
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 271

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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.
DOI : 10.2298/PIM1512271L
Classification : 54D20;54E35;46A19 54E99;54H20
Keywords: Stone's method, TVS-cone metric space, paracompact, metrizable, TVS-cone expansive homeomorphism 
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     author = {Shou Lin and Kedian Li and Ying Ge},
     title = {On the {Metrizability} of {TVS-Cone} {Metric} {Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {271 },
     publisher = {mathdoc},
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     doi = {10.2298/PIM1512271L},
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Shou Lin; Kedian Li; Ying Ge. On the Metrizability of TVS-Cone Metric Spaces. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 271 . doi: 10.2298/PIM1512271L

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