Sequences suffice for pointfree uniform completions

Graham Manuell

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arXiv · 2409.15569

Sequences suffice for pointfree uniform completions

Graham Manuell

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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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Graham Manuell. 2024-09-23. Sequences suffice for pointfree uniform completions. https://arxiv.org/abs/2409.15569

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