A topology for Engel expansions: evaluation and digit coding maps
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915549002334208 |
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| author | Ahn, Min Woong |
| author_facet | Ahn, Min Woong |
| contents | We develop a topological framework for Engel expansions that treats both directions of the correspondence between points of $(0,1]$ and nondecreasing digit sequences. We endow the sequence space with the product topology to study the evaluation map, and we fix a nonterminating digit algorithm to study the digit coding map. We also record the correspondence between cylinder sets and fundamental intervals, and give an application to Baire category results for functions of the digits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10850 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A topology for Engel expansions: evaluation and digit coding maps Ahn, Min Woong Dynamical Systems Number Theory Primary 37B10, Secondary 11A67, 54E52 We develop a topological framework for Engel expansions that treats both directions of the correspondence between points of $(0,1]$ and nondecreasing digit sequences. We endow the sequence space with the product topology to study the evaluation map, and we fix a nonterminating digit algorithm to study the digit coding map. We also record the correspondence between cylinder sets and fundamental intervals, and give an application to Baire category results for functions of the digits. |
| title | A topology for Engel expansions: evaluation and digit coding maps |
| topic | Dynamical Systems Number Theory Primary 37B10, Secondary 11A67, 54E52 |
| url | https://arxiv.org/abs/2510.10850 |