On Frink's metrization technique and applications

Tran Van An, Nguyen Van Dung

Published 2015-07-07Version 1

In this paper, we first give a simple counter-example to show again the gap of Frink's proof. Then we revise the Frink's metrization technique. As applications, we answer two conjectures posed by Berinde and Choban, calculate the induced metric from given $b$-metrics, and prove that the generalized metric in the sense of Branciari is metrizable. We also show that Banach contraction principles in $b$-metric spaces adn $g.m.s$'s may be deduced from Banach contraction principle in metric spaces.