Characterization of the algebraic difference of special affine Cantor sets
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912975535734784 |
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| author | Nowakowski, Piotr |
| author_facet | Nowakowski, Piotr |
| contents | We investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \in \mathbb{N}$, $l+r<p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval. As corollaries we give examples of Cantor sets and Cantorvals, which can be easily described using some positional numeral systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09546 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterization of the algebraic difference of special affine Cantor sets Nowakowski, Piotr Classical Analysis and ODEs 28A80, 05B10, 11A67 We investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \in \mathbb{N}$, $l+r<p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval. As corollaries we give examples of Cantor sets and Cantorvals, which can be easily described using some positional numeral systems. |
| title | Characterization of the algebraic difference of special affine Cantor sets |
| topic | Classical Analysis and ODEs 28A80, 05B10, 11A67 |
| url | https://arxiv.org/abs/2301.09546 |