Conditions for the difference set of a central Cantor set to be a Cantorval. Part II
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915876770414592 |
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| author | Nowakowski, Piotr |
| author_facet | Nowakowski, Piotr |
| contents | Let C(a) be the central Cantor set generated by a sequence a with terms in (0,1). It is known that the difference set C(a)-C(a) of C(a) can has one of three possible forms: a finite union of closed intervals, a Cantor set, or a Cantorval. In the previous paper there was proved a sufficient condition for the sequence a which implies that C(a) - C(a) is a Cantorval. In this paper we give different conditions for a sequence a which guarantee the same assertion. We also prove a corollary, which provides infinitely many new examples of Cantorvals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08102 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditions for the difference set of a central Cantor set to be a Cantorval. Part II Nowakowski, Piotr Classical Analysis and ODEs 28A12, 11B13 Let C(a) be the central Cantor set generated by a sequence a with terms in (0,1). It is known that the difference set C(a)-C(a) of C(a) can has one of three possible forms: a finite union of closed intervals, a Cantor set, or a Cantorval. In the previous paper there was proved a sufficient condition for the sequence a which implies that C(a) - C(a) is a Cantorval. In this paper we give different conditions for a sequence a which guarantee the same assertion. We also prove a corollary, which provides infinitely many new examples of Cantorvals. |
| title | Conditions for the difference set of a central Cantor set to be a Cantorval. Part II |
| topic | Classical Analysis and ODEs 28A12, 11B13 |
| url | https://arxiv.org/abs/2307.08102 |