Continuity of the continued fraction mapping revisited

期刊论文
发表日期：

2025年3月4日

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Min Woong Ahn

摘要

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 $\mathbb {R}$ $R$ , the continued fraction mapping is a homeomorphism onto the product space $\mathbb {N}^{\mathbb {N}}$ $N^{N}$ , where $\mathbb {N}$ $N$ 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.