Max(dL) revisited

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-08-30 DOI:10.1016/j.topol.2024.109057

Papiya Bhattacharjee

引用次数: 0

Abstract

This article studies different topological properties of the space of maximal d-elements of an M-frame with a unit. We characterize when the space $M a x (d L)$ is Hausdorff, answering the question posed in [2]. We also characterize other topological properties of $M a x (d L)$ , namely zero-dimensional, discrete, and clopen π-base. The concept of weak-component elements is introduced here, as a generalized idea from the theory of rings, which is essential in the study of d-semiprime frames.

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重温最大值（dL）

本文研究了有单元的 M 框架的最大 d 元素空间的不同拓扑性质。我们描述了 Max(dL) 空间的 Hausdorff 特性，回答了 [2] 中提出的问题。我们还描述了 Max(dL) 的其他拓扑性质，即零维、离散和 clopen π-base。这里引入了弱分量元素的概念，它是环理论中的一个广义概念，在 d-semiprime 框架的研究中至关重要。

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

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.

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