序列足以满足无点均匀补全

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-19 DOI:10.1112/jlms.70272

Graham Manuell

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引用次数: 0

摘要

度量空间的补全通常用柯西序列构造。然而，这并不适用于一般的均匀空间，在那里必须使用柯西过滤器或网。无点拓扑中的情况更直接：一致区域的正确补全确实可以作为柯西序列区域的商来获得。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Sequences suffice for pointfree uniform completions

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Sequences suffice for pointfree uniform completions

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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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.