亚历山德罗夫副本的断线

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-10-01 DOI:10.4995/agt.2021.14602

Papiya Bhattacharjee, Michelle L. Knox, W. W. McGovern

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引用次数: 2

摘要

在[2]中证明了自然界的Čech-Stone紧化的Alexandroff副本并不是完全断开的。提出了一个问题，即一个非离散的极不连通空间的亚历山德罗夫副本是否可以是极不连通的。我们对这个问题的回答是肯定的;范杜文的一个例子很有意义。在一个稍微不同的方向上，我们还描述了一个空间的Alexandroff重复什么时候是p空间，以及什么时候是几乎p空间。

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Disconnection in the Alexandroff duplicate

It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of van Douwen is significant. In a slightly different direction we also characterize when the Alexandroff duplicate of a space is a P-space as well as when it is an almost P-space.

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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.