Hausdorff distance of univoque sets

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-26 DOI:10.1016/j.topol.2025.109378

Yi Cai , Vilmos Komornik

引用次数: 0

Abstract

Since their introduction by Rényi [21], expansions in non-integer bases have been investigated abundantly. It was discovered by Erdős et al. [10], [11] that, contrary to the case of integer bases, the sets of numbers with a unique expansion have a surprisingly complex structure. The present paper is devoted to the continuity properties of these sets with respect to the base.

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唯一集的豪斯多夫距离

自rsamunyi[21]引入以来，对非整数基的展开式进行了大量的研究。Erdős等人[10]，[11]发现，与整数基的情况相反，具有唯一展开的数集具有令人惊讶的复杂结构。本文研究了这些集合关于基的连续性。

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.