Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-12 DOI:10.1007/s43037-024-00329-x

Yang Deng, Marcel de Jeu

引用次数: 0

Abstract

We show that, for a class of locally solid topologies on vector lattices, a topologically convergent net has an embedded sequence that is unbounded order convergent to the same limit. Our result implies, and often improves, many of the known results in this vein in the literature. A study of metrisability and submetrisability of locally solid topologies on vector lattices is included.

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向量网格中拓扑收敛网的嵌入式无界阶收敛序列

我们证明，对于向量网格上的一类局部固态拓扑，拓扑收敛网有一个内嵌序列，该序列无界阶收敛到相同的极限。我们的结果暗示并常常改进了文献中许多这方面的已知结果。研究还包括对向量网格上局部实体拓扑的可元性和次元性的研究。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.