Binary metrics

Samer Assaf; Tom Cuchta; Matt Insall

doi:10.1016/j.topol.2020.107116

Binary metrics

Samer Assaf, Tom Cuchta, Matt Insall

Mathematic and Natural Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Article number	107116
Journal	Topology and its Applications
Volume	274
DOIs	https://doi.org/10.1016/j.topol.2020.107116
State	Published - 1 Apr 2020

Keywords

Binary metric
Generalized metric
Partial metric

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10.1016/j.topol.2020.107116

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AU - Insall, Matt

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AB - 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.

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KW - Generalized metric

KW - Partial metric

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DO - 10.1016/j.topol.2020.107116

M3 - Article

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VL - 274

JO - Topology and its Applications

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Binary metrics

Abstract

Keywords

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