Continuity of the continued fraction mapping revisited
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915198986616832 |
|---|---|
| author | Ahn, Min Woong |
| author_facet | Ahn, Min Woong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuity of the continued fraction mapping revisited Ahn, Min Woong Number Theory Classical Analysis and ODEs Primary 11A55, Secondary 26A15 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. |
| title | Continuity of the continued fraction mapping revisited |
| topic | Number Theory Classical Analysis and ODEs Primary 11A55, Secondary 26A15 |
| url | https://arxiv.org/abs/2404.18853 |