On certain star versions of a Ufin-type selection principle

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-07-31 DOI:10.1016/j.topol.2024.109029

引用次数: 0

Abstract

The star versions of the selection principle $U_{fin} (O, Ω)$ , namely $U_{fin}^{⁎} (O, Ω)$ , $S S_{fin}^{⁎} (O, Ω)$ and ${}^{⁎}U_{fin} (O, Ω)$ are studied. We explore ramifications concerning critical cardinalities. Quite a few interesting observations are obtained while dealing with the Isbell-Mrówka spaces, Niemytzki plane and Alexandroff duplicates. Properties like monotonically normal and locally countable cellularity (introduced here) play an important role in our investigation. We study games corresponding to $U_{fin} (O, Ω)$ and its star variants which have not been investigated in prior works. Some open problems are posed.

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关于乌芬型选择原理的某些星型版本

我们研究了选择原则的星形版本，即、和。我们探讨了临界心性的影响。在处理伊斯贝尔-姆鲁夫卡空间、尼米兹基平面和亚历山德罗夫复数时，我们获得了许多有趣的观察结果。单调正态性和局部可数蜂窝性（在此引入）等属性在我们的研究中发挥了重要作用。我们研究了与之相对应的博弈及其星形变体，这些在以前的著作中还没有研究过。我们还提出了一些悬而未决的问题。

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.