Countable dense homogeneity and topological groups

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-11 DOI:10.1016/j.topol.2025.109537

Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy

引用次数: 0

Abstract

Building on results of Medvedev, we construct a

ZFC

example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of

Z^{ω}

of size

b

that is a λ-set. We also conjecture that every countable dense homogeneous Baire topological group with no isolated points contains a copy of the Cantor set, and give a proof in a very special case.

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可数密集同质性与拓扑群

在梅德韦杰夫的结果的基础上，我们构造了一个非波兰拓扑群的ZFC例子，它是可数的密集齐次的。我们的例子是一个大小为b的Zω的密集子群，它是一个λ集合。我们还推测了每一个无孤立点的可数密集齐次Baire拓扑群都存在一个Cantor集合的副本，并给出了一个非常特殊的证明。

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.