Binary metrics

Authors

Samer Assaf
Tom Cuchta, Marshall UniversityFollow
Matt Insall

Document Type

Article

Publication Date

4-2020

Abstract

We define a binary metric as a symmetric, distributive lattice ordered magma-valued function of two variables, satisfying a “triangle inequality”. Using the notion of a Kuratowski topology, in which topologies are specified by closed sets rather than open sets, we prove that every topology is induced by a binary metric. We conclude with a discussion on the relation between binary metrics and some separation axioms.

Comments

Copyright © 2020 Elsevier B.V. All rights reserved.

Recommended Citation

Assaf, S., Cuchta, T., & Insall, M. (2020). Binary metrics. Topology and its Applications, 274, 107116. https://doi.org/10.1016/j.topol.2020.107116