On the metrizability of TVS-cone metric spaces | Zendy

Shou Lin | Zendy; LI Ke-dian | Zendy; Ying Ge | Zendy

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On the metrizability of TVS-cone metric spaces

Author(s) -

Shou Lin,

LI Ke-dian,

Ying Ge

Publication year - 2015

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1512271l

Subject(s) - metric space , paracompact space , mathematics , injective metric space , convex metric space , topology (electrical circuits) , cone (formal languages) , pure mathematics , expansive , metric (unit) , intrinsic metric , dual cone and polar cone , uniform continuity , mathematical analysis , geometry , combinatorics , physics , hausdorff space , algorithm , operations management , compressive strength , regular polygon , economics , thermodynamics

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 obtain 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.

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