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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.19454 |
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| _version_ | 1866916920669765632 |
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| author | Głąb, Szymon Kula, Mateusz |
| author_facet | Głąb, Szymon Kula, Mateusz |
| contents | We study sets $E(Σ,q)=\left\{\sum_{i=1}^\infty σ_iq^i\colon(σ_i)\inΣ^{\mathbb N}\right\}$ for a finite set $Σ\subset \mathbb R$ and $q\in(0,1)$. Under the assumption $q|Σ|=1$ we prove several new equivalent conditions for $E(Σ,q)$ to contain an interval. We give a full characterization, if additionally $|Σ|$ is prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kenyon Theorem Revisited Głąb, Szymon Kula, Mateusz General Topology 40A We study sets $E(Σ,q)=\left\{\sum_{i=1}^\infty σ_iq^i\colon(σ_i)\inΣ^{\mathbb N}\right\}$ for a finite set $Σ\subset \mathbb R$ and $q\in(0,1)$. Under the assumption $q|Σ|=1$ we prove several new equivalent conditions for $E(Σ,q)$ to contain an interval. We give a full characterization, if additionally $|Σ|$ is prime. |
| title | Kenyon Theorem Revisited |
| topic | General Topology 40A |
| url | https://arxiv.org/abs/2508.19454 |