Σ积的双离散性和无限积的不可还原性

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-08-12 DOI:10.1016/j.topol.2024.109032

Yasushi Hirata, Yukinobu Yajima

引用次数: 0

摘要

本文包括两个主要结果。双离散性是 D 空间的一个众所周知的广义。第一个结果是紧凑度量空间的每个 Σ 积都是双离散的。aD 属性是 D 空间的另一种广义化，它意味着不可还原性。第二个是 N 的 ω1 多份的乘积 Nω1 是不可还原的，其中 N 表示无限可数离散空间。

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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Dual discreteness of Σ-products and irreducibility of infinite products

This paper includes two main results. Dual discreteness is a well known generalization of D-spaces. The first one is that every Σ-product of compact metric spaces is dually discrete. The property aD is another generalization of D-spaces, and it implies irreducibility. The second one is that the product $N^{ω_{1}}$ of $ω_{1}$ many copies of $N$ is irreducible, where $N$ denotes an infinite countable discrete space.

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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.

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