On the modular metric completion

Olivier Olela-Otafudu; Tlotlo Odacious Phawe

doi:10.4995/agt.2025.23431

On the modular metric completion

Olivier Olela-Otafudu

https://orcid.org/0000-0001-9593-7899

South Africa

University of Limpopo

Department of Mathematics and Applied Mathematics

Tlotlo Odacious Phawe

https://orcid.org/0000-0003-2837-8147

South Africa

North-West University

School of Mathematical and Statistical Sciences

Submitted: 2025-02-21

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Accepted:

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Published: 2025-10-01

DOI: https://doi.org/10.4995/agt.2025.23431

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Keywords:

modular completion, isometry, modular convergence, modular metric

Supporting agencies:

This research was not funded

Abstract:

The purpose of this paper is to present the construction of the completion of a set equipped with a modular metric that we call the modular completion. We show for instance that any set equipped with a modular metric has a modular completion. Moreover, it turns out that the modular completion is unique up to isometry.

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