Intermediate dimensions of complementary sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914159353921536 |
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| author | Angelini, Nicolas Molter, Ursula |
| author_facet | Angelini, Nicolas Molter, Ursula |
| contents | Given a positive, non-increasing sequence $a$ with finite sum equal to $1$, we consider the family of all closed subsets of $[0,1]$ whose complementary open intervals have lengths given by a rearrangement of the sequence $a$. We study the full range of possible $θ$-intermediate dimensions of these sets and, under suitable assumptions on the sequence, we show that this range forms a closed interval, whose endpoints we compute explicitly. This paper fills a gap in the literature concerning the dimensional properties of complementary sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intermediate dimensions of complementary sets Angelini, Nicolas Molter, Ursula Classical Analysis and ODEs 28A80, 28A75, Given a positive, non-increasing sequence $a$ with finite sum equal to $1$, we consider the family of all closed subsets of $[0,1]$ whose complementary open intervals have lengths given by a rearrangement of the sequence $a$. We study the full range of possible $θ$-intermediate dimensions of these sets and, under suitable assumptions on the sequence, we show that this range forms a closed interval, whose endpoints we compute explicitly. This paper fills a gap in the literature concerning the dimensional properties of complementary sets. |
| title | Intermediate dimensions of complementary sets |
| topic | Classical Analysis and ODEs 28A80, 28A75, |
| url | https://arxiv.org/abs/2412.12999 |