关于区域设置中的门格和几乎门格属性

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-04-01 DOI:10.4995/AGT.2021.14915

Tilahun Bayih, T. Dube, O. Ighedo

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引用次数: 1

摘要

Menger和几乎Menger属性被扩展到区域设置。前者的扩展是保守的(即当且仅当空间是门格尔作为场所)，后者对于清醒的td空间是保守的。非空间门格尔(因此几乎是门格尔)区域确实存在，因此扩展真正超越了拓扑概念。我们还考虑投影门格尔区域，并表明，正如在空间中一样，当一个区域恰好是Lindelöf和投影门格尔时，它就是门格尔。考虑了这些属性沿局部映射(通过直接图像或回拉)的转移。2010 msc: 06d22;54 c05;54 d20开头。

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On the Menger and almost Menger properties in locales

The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober TD-spaces. Non-spatial Menger (and hence almost Menger) locales do exist, so that the extensions genuinely transcend the topological notions. We also consider projectively Menger locales, and show that, as in spaces, a locale is Menger precisely when it is Lindelöf and projectively Menger. Transference of these properties along localic maps (via direct image or pullback) is considered. 2010 MSC: 06D22; 54C05; 54D20.

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.