Work

Sequences suffice for pointfree uniform completions

Year: 2025

Type: article

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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70272

Author: Graham Manuell

Institution: Stellenbosch University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Universidade de Coimbra, Ministério da Ciência, Tecnologia e Ensino Superior, Fundação para a Ciência e a Tecnologia