Continuity of the continued fraction mapping revisited

IF 0.5 4区 数学 Q3 MATHEMATICS
Min Woong Ahn
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引用次数: 0

Abstract

The continued fraction mapping maps a number in the interval [0, 1) to the sequence of its partial quotients. When restricted to the set of irrationals, which is a subspace of the Euclidean space \(\mathbb {R}\), the continued fraction mapping is a homeomorphism onto the product space \(\mathbb {N}^{\mathbb {N}}\), where \(\mathbb {N}\) is a discrete space. In this short note, we examine the continuity of the continued fraction mapping, addressing both irrational and rational points of the unit interval.

重新讨论连分数映射的连续性
连分数映射将区间[0,1)内的一个数映射到它的部分商序列。当限定于无理数集合,即欧几里得空间\(\mathbb {R}\)的子空间时,连分式映射是到积空间\(\mathbb {N}^{\mathbb {N}}\)的同胚映射,其中\(\mathbb {N}\)是离散空间。在这篇简短的笔记中,我们研究了连分数映射的连续性,处理了单位区间的无理点和有理点。
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
Archiv der Mathematik
Archiv der Mathematik 数学-数学
CiteScore
1.10
自引率
0.00%
发文量
117
审稿时长
4-8 weeks
期刊介绍: Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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