局部实收敛空间中的可数条件

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-09-15 DOI:10.1007/s43034-025-00433-5

Eugene Bilokopytov, Viktor Bohdanskyi, Jan Harm van der Walt

引用次数: 0

摘要

研究了阿基米德向量格上局部固体收敛结构的（强）第一可数性。在其他结果中，我们分别描述了相对一致，有序和\(\sigma\) -阶收敛是（强）第一可数的向量格。指出了在这些收敛结构的背景下序列参数有效性的含义。

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Countability conditions in locally solid convergence spaces

We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively uniform-, order-, and \(\sigma\)-order convergence, respectively, is (strongly) first countable. The implications for the validity of sequential arguments in the contexts of these convergence structures are pointed out.

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.