Only 3-generalized metric spaces have a compatible symmetric topology

Tomonari Suzuki; Badriah Alamri; Misako Kikkawa

doi:10.1515/math-2015-0048

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Only 3-generalized metric spaces have a compatible symmetric topology

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Only 3-generalized metric spaces have a compatible symmetric topology

Tomonari Suzuki, Badriah Alamri and Misako Kikkawa

Open mathematics (Warsaw, Poland), Vol.13(1), pp.510-517

04/09/2015

DOI: https://doi.org/10.1515/math-2015-0048

Abstract

Mathematics

Physical Sciences

Science & Technology

We prove that every 3-generalized metric space is metrizable. We also show that for any v with v >= 4, not every v-generalized metric space has a compatible symmetric topology.

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Title: Only 3-generalized metric spaces have a compatible symmetric topology
Creators - without role: Tomonari Suzuki - Kyushu Institute of Technology
Badriah Alamri - King Abdulaziz University
Misako Kikkawa - Saitama University
Publication Details: Open mathematics (Warsaw, Poland), Vol.13(1), pp.510-517
Publisher: Walter de Gruyter
Number of pages: 8
Grant note: KAU 25400141 / JSPS KAKENHI Grant from Japan Society for the Promotion of Science 35-130-35-HiCi / Deanship of Scientific Research (DSR), King Abdulaziz University
Identifiers: 9932947608331
Academic Unit: University of Jeddah
Language: English
Resource Type: Journal article