Two topologies on the set of minimal prime elements of a continuous frame

IF 0.5 3区 数学 Q3 MATHEMATICS
Chongxia Lu, Qingguo Li
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引用次数: 0

Abstract

In this paper, we discuss the properties of the hull-kernel topology and the inverse topology on the set [Formula: see text] of minimal prime elements of a continuous frame [Formula: see text]. We prove that the set [Formula: see text] endowed with the hull-kernel topology and the inverse topology, respectively, is a [Formula: see text]-space. Moreover, we obtain that there is a bijective correspondence between the set [Formula: see text] of all maximal Scott open filters of [Formula: see text] and the set [Formula: see text] when [Formula: see text] is a stably continuous frame. By considering the bijective correspondence between the sets [Formula: see text] and [Formula: see text], we propose some sufficient conditions for the topological spaces [Formula: see text] endowed with the hull-kernel topology and the inverse topology, respectively, to be sober, Hausdorff, compact, extremely disconnected and zero-dimensional spaces, respectively, when [Formula: see text] is a stably continuous frame.
连续框架最小素元素集合上的两种拓扑
本文讨论了连续框架最小素元集[公式:见文]上的壳核拓扑和逆拓扑的性质。我们证明了分别具有壳核拓扑和逆拓扑的集合[公式:见文]是一个[公式:见文]空间。并且,我们得到了当[Formula: see text]为稳定连续帧时,[Formula: see text]的所有极大Scott开放滤波器的集合[Formula: see text]与集合[Formula: see text]之间存在双射对应。通过考虑集合[公式:见文]和集合[公式:见文]之间的双射对应关系,给出了当[公式:见文]是稳定连续坐标系时,具有壳核拓扑和逆拓扑的拓扑空间[公式:见文]分别为清醒空间、Hausdorff空间、紧空间、极度不连通空间和零维空间的充分条件。
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
CiteScore
1.50
自引率
12.50%
发文量
226
审稿时长
4-8 weeks
期刊介绍: The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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