拓扑mv -代数的一些结果

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-07 DOI:10.1016/j.topol.2025.109328

Leyao Yin , Lihong Xie , Jiang Yang

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引用次数: 0

摘要

本文首先给出了满足开条件的有限拓扑mv -代数的等价刻画。此外，我们还研究了具有开条件的拓扑mv -代数的拓扑同构定理和其他相关结果。然后研究了拓扑mv -代数的初始拓扑。此外，我们引入了原mv -代数的概念，以及在原mv -代数A上集合论滤波器族ω(A)上的两个操作∔和‘，这些操作使（ω(A),∔,’，↑0）成为原mv -代数。特别是，我们建立了类别PMV和类别TPMV之间的关系。

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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Some results on topological MV-algebras

First of all, in this paper, we give an equivalent characterization for a finite topological MV-algebra satisfying the open condition. In addition, we investigate the topological isomorphism theorems and other related results of topological MV-algebras with the open condition. Then we study the initial topology of topological MV-algebras. Moreover, we introduce the concept of proto-MV-algebras and two operations ∔ and ′ on the family

ω (A)

of set-theoretic filters on proto-MV-algebra A. These operations make

(ω (A), ∔,', ↑ 0)

a proto-MV-algebra. Especially, we establish a relationship between the category

PMV

and the category

TPMV

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.