半近似空间和规范性

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-06-11 DOI:10.1016/j.topol.2024.108990

Khulod Almontashery , Paul J. Szeptycki

引用次数: 0

摘要

我们考虑了正则性与半近似性之间的关系。我们给出了一个不是半近似的第一可数局部紧凑道克空间的一致例子，以及两个半近似非正则空间的 ZFC 例子。这回答了尼科斯的一个问题。其中一个例子是 (ω+1)×ω1 的子空间。相反，我们证明了 ω1 的有限幂的每一个正态子空间都是半近似的。

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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Semi-proximal spaces and normality

We consider the relationship between normality and semi-proximality. We give a consistent example of a first countable locally compact Dowker space that is not semi-proximal, and two ZFC examples of semi-proximal non-normal spaces. This answers a question of Nyikos. One of the examples is a subspace of $(ω + 1) \times ω_{1}$ . In contrast, we show that every normal subspace of a finite power of $ω_{1}$ is semi-proximal.

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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.