由正方形和AD族构成的空间的强变形性质

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2023-10-02 DOI:10.4995/agt.2023.18504

William Chen-Mertens, César Corral-Rojas, Paul J. Szeptycki

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引用次数: 0

摘要

我们使用由组合对象定义的空间来回答Arhangel'ski的问题。我们首先建立了由□(κ)构造的空间的进一步收敛性质，表明它对于有限集和非w空间的w空间是fr切特-尤里松的。我们还表明，在附加的假设下，它可能不是双序的，因此提供了一个绝对fr α1空间不是双等的一致例子。此外，如果我们不要求空间为α1，我们可以从自然数的几乎不相交的子集族中构造一个非等等的可数绝对fr空间的ZFC例子。

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Strong Fréchet properties of spaces constructed from squares and AD families

We answer questions of Arhangel'skiĭ using spaces defined from combinatorial objects. We first establish further convergence properties of a space constructed from □ ( κ ) showing it is Fréchet-Urysohn for finite sets and a w-space that is not a W-space. We also show that under additional assumptions it may be not bi-sequential, and so providing a consistent example of an absolutely Fréchet α1 space that is not bisequential. In addition, if we do not require the space being α1, we can construct a ZFC example of a countable absolutely Fréchet space that is not bisequential from an almost disjoint family of subsets of the natural numbers.

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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.