Yet Another Generalization of The Notion of a Metric Space

Seyed Mohammad Amin Khatami, Madjid Mirzavaziri

Published 2020-09-02Version 1

A generalization of the triangle inequality is introduced by a mapping similar to a t-conorm mapping. This generalization leads us to a notion for which we use the $\star$-metric terminology. We are interested in the topological space induced by a $\star$-metric. Considering some examples of non-trivial $\star$-metrizable topological spaces, we also study the product topology for a finite family of $\star$-metrizable topological spaces.