We prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.
@article{bwmeta1.element.doi-10_1515_math-2015-0048,
author = {Tomonari Suzuki and Badriah Alamri and Misako Kikkawa},
title = {Only 3-generalized metric spaces have a compatible symmetric topology},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {06594244},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0048}
}
Tomonari Suzuki; Badriah Alamri; Misako Kikkawa. Only 3-generalized metric spaces have a compatible symmetric topology. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0048/
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