在可数序数上的群

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-13 DOI:10.1016/j.topol.2025.109480

Stepan Milošević , Stevo Todorčević

引用次数: 0

摘要

研究了由可数序数上的行走特征构造的拓扑群。引入了由ρ1和ρ3构造的两个群，证明了它们都是fracimcheet，不可度量的，并且证明了由ρ1构造的拓扑群在特征ω1的拓扑群中具有最大的Tukey类型。我们还考虑了[12]中引入的与ρ2相关的群，并证明了在某些集合论假设下，该群不具有极大的Tukey类型。

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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Groups from walks on countable ordinals

This paper deals with topological groups constructed from characteristics of walks on countable ordinals. We introduce two groups, constructed from

ρ_{1}

and

ρ_{3}

, and show they are both Fréchet, non-metrizable and that the topological group constructed from

ρ_{1}

has the maximal Tukey type among topological groups of character

ω_{1}

. We also consider the group associated with

ρ_{2}

introduced in [12] and show that under some set-theoretic assumptions the group does not have the maximal Tukey type.

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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.