Uniqueness and topological properties of number representation
Let b be a complex number with |b| > 1 and let D be a finite subset of the complex plane C such that 0 ∊ D and card D ≥ 2. A number z is representable by the system (D, b) if z = Σajbj , where aj ∊ D. We denote by F the set of numbers which are representable by (D, b) with M = −1. The set W consi...
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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2004 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/124622 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Uniqueness and topological properties of number representation / O. Dovgoshey, O. Martio, V. Ryazanov, M. Vuorinen // Український математичний вісник. — 2004. — Т. 1, № 3. — С. 331-348. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862555246829502464 |
|---|---|
| author | Dovgoshey, O. Martio, O. Ryazanov, V. Vuorinen, M. |
| author_facet | Dovgoshey, O. Martio, O. Ryazanov, V. Vuorinen, M. |
| citation_txt | Uniqueness and topological properties of number representation / O. Dovgoshey, O. Martio, V. Ryazanov, M. Vuorinen // Український математичний вісник. — 2004. — Т. 1, № 3. — С. 331-348. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | Let b be a complex number with |b| > 1 and let D be a finite subset of the complex plane C such that 0 ∊ D and card D ≥ 2. A number z is representable by the system (D, b) if z = Σajbj , where aj ∊ D. We denote by F the set of numbers which are representable by (D, b) with M = −1. The set W consists of numbers that are (D, b) representable with aj = 0 for all negative j. Let F1 be a set of numbers in F that can be uniquely represented by (D, b). It is shown that: The set of all extreme points of F is a subset of F1. If 0 ∊ F1, then W is discrete and closed. If b ∊ {z : |z| > 1}\D′, where D′ is a finite or countable set associated with D and W is discrete and closed, then 0 ∊ F1. For a real number system (D, b), F is homeomorphic to the Cantor set C iff F\F1 is nowhere dense subset of R.
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| first_indexed | 2025-11-25T21:46:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124622 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-11-25T21:46:19Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dovgoshey, O. Martio, O. Ryazanov, V. Vuorinen, M. 2017-09-30T11:12:21Z 2017-09-30T11:12:21Z 2004 Uniqueness and topological properties of number representation / O. Dovgoshey, O. Martio, V. Ryazanov, M. Vuorinen // Український математичний вісник. — 2004. — Т. 1, № 3. — С. 331-348. — Бібліогр.: 12 назв. — англ. 1810-3200 2000 MSC. 11A67. https://nasplib.isofts.kiev.ua/handle/123456789/124622 Let b be a complex number with |b| > 1 and let D be a finite subset of the complex plane C such that 0 ∊ D and card D ≥ 2. A number z is representable by the system (D, b) if z = Σajbj , where aj ∊ D. We denote by F the set of numbers which are representable by (D, b) with M = −1. The set W consists of numbers that are (D, b) representable with aj = 0 for all negative j. Let F1 be a set of numbers in F that can be uniquely represented by (D, b). It is shown that: The set of all extreme points of F is a subset of F1. If 0 ∊ F1, then W is discrete and closed. If b ∊ {z : |z| > 1}\D′, where D′ is a finite or countable set associated with D and W is discrete and closed, then 0 ∊ F1. For a real number system (D, b), F is homeomorphic to the Cantor set C iff F\F1 is nowhere dense subset of R. en Інститут прикладної математики і механіки НАН України Український математичний вісник Uniqueness and topological properties of number representation Article published earlier |
| spellingShingle | Uniqueness and topological properties of number representation Dovgoshey, O. Martio, O. Ryazanov, V. Vuorinen, M. |
| title | Uniqueness and topological properties of number representation |
| title_full | Uniqueness and topological properties of number representation |
| title_fullStr | Uniqueness and topological properties of number representation |
| title_full_unstemmed | Uniqueness and topological properties of number representation |
| title_short | Uniqueness and topological properties of number representation |
| title_sort | uniqueness and topological properties of number representation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124622 |
| work_keys_str_mv | AT dovgosheyo uniquenessandtopologicalpropertiesofnumberrepresentation AT martioo uniquenessandtopologicalpropertiesofnumberrepresentation AT ryazanovv uniquenessandtopologicalpropertiesofnumberrepresentation AT vuorinenm uniquenessandtopologicalpropertiesofnumberrepresentation |