On cofinite topologies on posets, chains in subfit frames, and subfit irreducible frames

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-01 DOI:10.1016/j.topol.2025.109380

M. Andrew Moshier , Aleš Pultr

引用次数: 0

Abstract

We prove that (1) each well-ordered chain is a dense sublocale of a subfit frame, and (2) that an irreducible frame (a frame that cannot be decomposed into two smaller closed sublocales) can be subfit (although it cannot be fit or even prefit). The basic tool is to use order-cofinite topologies on posets (also known as weak topologies); we discuss these in some more detail, for instance showing their relation with the Bruns-Lakser hull.

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关于偏序集、子拟合框架中的链和子拟不可约框架上的有限拓扑

我们证明了(1)每个良序链都是子拟合框架的密集子区域，(2)不可约框架（不能分解为两个较小的封闭子区域）可以是子拟合的（尽管它不能拟合甚至不能预拟）。基本工具是在偏序集上使用序有限拓扑（也称为弱拓扑）；我们将更详细地讨论这些问题，例如，说明它们与布伦斯-莱克塞尔船体的关系。

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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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.