Sequences suffice for pointfree uniform completions

Abstract Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy sequences.

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Publication Details

Journal
Journal of the London Mathematical Society
Published
2025-08-01
DOI
https://doi.org/10.1112/jlms.70272
Primary Topic
Advanced Algebra and Logic
Type
article
Field-Weighted Citation Impact
0.00

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article

Sequences suffice for pointfree uniform completions

Graham Manuell
Journal of the London Mathematical Society
Advanced Algebra and Logic
article

Sequences suffice for pointfree uniform completions

Graham Manuell
article en

Abstract

Abstract Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy sequences.

Journal of the London Mathematical SocietyVol. 112(2)
Stellenbosch University (ZA)
Universidade de Coimbra
Openalex Percentile: Top 77%
Advanced Algebra and Logic
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Sequences suffice for pointfree uniform completions — Graham Manuell · Journal of the London Mathematical Society (2025) | TGRS Research Map | TGRS