公制 σ 框架的均匀局部连通性和完备性

Pub Date : 2023-12-01 DOI:10.1515/ms-2023-0100

I. Naidoo

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引用次数: 0

摘要

摘要我们将局部连通性和均匀局部连通性的概念扩展到度量 σ 框架的范畴 MσFrm。我们提供了局部连通的度量 σ 框架的均匀局部连通反射的构造。我们还讨论了完整的度量 σ-框架，并证明了在 MσFrm 范畴中度量 σ-框架的完备性的存在。

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Uniform Local Connectedness and Completion of Metric σ-Frames

ABSTRACT We extend the notion of local connectedness and uniform local connectedness to the category MσFrm of metric σ-frames. We provide the construction of the uniformly locally connected reflection of a locally connected metric σ-frame. We also discuss complete metric σ-frames and show the existence of a completion for a metric σ-frame in the category MσFrm.

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