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<p>In the late ‘90s, Banaschewski and Vermeulen showed that any localic group is complete in its two-sided uniformity. In this paper, we provide a method of constructing extensions of localic groups. The raison d’être of this paper, however, is to show using generators and relations that if the left and the right uniformity coincide, then the localic group must be complete.</p>

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On the completeness of localic groups via generators and relations

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  • 发表日期：

    2025年6月19日

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  • Simo S. Mthethwa,
  • Onesipho Ntombela

摘要

In the late ‘90s, Banaschewski and Vermeulen showed that any localic group is complete in its two-sided uniformity. In this paper, we provide a method of constructing extensions of localic groups. The raison d’être of this paper, however, is to show using generators and relations that if the left and the right uniformity coincide, then the localic group must be complete.