Representations of bornologies

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2022-04-01 DOI:10.4995/agt.2022.16405

H. Pajoohesh

引用次数: 0

Abstract

Bornologies abstract the properties of bounded sets of a metric space. But there are unbounded bornologies on a metric space like $\mathcal{P}(\RR)$ with the Euclidean metric. We show that by replacing $[0,\infty)$ with a partially ordered monoid every bornology is the set of bounded subsets of a generalized metric mapped into a partially ordered monoid. We also prove that the set of bornologies on a set is the join completion of the equivalence classes of a relation on the power set of the set.

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bornology的表示

Bornologies抽象了度量空间的有界集合的性质。但是在度量空间上有无界的边界比如$\mathcal{P}(\RR)$和欧几里得度规。通过用偏序单群替换$[0,\infty)$，我们证明了每一个本体都是映射到偏序单群的广义度量的有界子集的集合。我们还证明了集合上的本体集是一个关系在该集合的幂集上的等价类的连接补全。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.