Fractal dimension of the boundary of cantorvals
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Date
2024
Authors
Karvatskyi, Dmytro
Journal Title
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Volume Title
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Abstract
We say that a Cantorval ๐ is achievable if there exists a convergent positive series ฮฃ๏ธ ๐ข๐ such that ๐ = ๐ธ(๐ข๐). Taking into account the above theorem, there naturally arises the question: Is the boundary ๐๐ถ for an arbitrary Cantorval ๐ a fractal set?
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Keywords
the closed bounded set, singletons, the interior, Hausdorff dimension, conference abstracts
Citation
Karvatskyi D. M. Fractal dimension of the boundary of Cantorvals / D. M. Karvatskyi // XII ะัะตัะบัะฐัะฝััะบะฐ ะฝะฐัะบะพะฒะฐ ะบะพะฝัะตัะตะฝัiั ะผะพะปะพะดะธั
ะผะฐัะตะผะฐัะธะบiะฒ, ะะธัะฒ, 9-11 ััะฐะฒะฝั 2024 ั. : [ะทะฑััะฝะธะบ ัะตะท /ะพัะณะบะพะผ.: ะะปะธะฑะพะฒะตัั ะ. ะ. ัะฐ ัะฝ.] ; ะะฐัiะพะฝะฐะปัะฝะธะน ัะฝiะฒะตััะธัะตั ะะธัะฒะพ-ะะพะณะธะปัะฝััะบะฐ ะฐะบะฐะดะตะผiั" [ัะฐ ัะฝ.]. - [ะะธัะฒ : ะฑ. ะฒ.], 2024. - C. 69.