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arXiv · 2404.18853

Continuity of the continued fraction mapping revisited

Min Woong Ahn
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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.

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Min Woong Ahn. 2024-04-29. Continuity of the continued fraction mapping revisited. https://doi.org/10.1007/s00013-025-02102-4

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