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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title = "Binary metrics",

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.",

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T1 - Binary metrics

AU - Assaf, Samer

AU - Cuchta, Tom

AU - Insall, Matt

PY - 2020/4/1

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N2 - 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.

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.

KW - Binary metric

KW - Generalized metric

KW - Partial metric

UR - https://www.scopus.com/pages/publications/85079647132

U2 - 10.1016/j.topol.2020.107116

DO - 10.1016/j.topol.2020.107116

M3 - Article

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SN - 0166-8641

VL - 274

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 107116

ER -

Binary metrics

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Keywords

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