The comb-like representations of cellular ordinal balleans
Given two ordinal \(\lambda\) and \(\gamma\), let \(f:[0,\lambda) \rightarrow [0,\gamma)\) be a function such that, for each \(\alpha<\gamma\), \(\sup\{f(t): t\in[0, \alpha]\}<\gamma.\) We define a mapping \(d_{f}: [0,\lambda)\times [0,\lambda) \longrightarrow [0,\gamma)\) by the rule...
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| Дата: | 2016 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2016
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/200 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-2002016-07-12T10:09:40Z The comb-like representations of cellular ordinal balleans Protasov, Igor Protasova, Ksenia ultrametric space, cellular ballean, ordinal ballean, \((\lambda,\gamma)-\)comb 54A05, 54E15, 54E30 Given two ordinal \(\lambda\) and \(\gamma\), let \(f:[0,\lambda) \rightarrow [0,\gamma)\) be a function such that, for each \(\alpha<\gamma\), \(\sup\{f(t): t\in[0, \alpha]\}<\gamma.\) We define a mapping \(d_{f}: [0,\lambda)\times [0,\lambda) \longrightarrow [0,\gamma)\) by the rule: if \(x<y\) then \(d_{f}(x,y)= d_{f}(y,x)= \sup\{f(t): t\in(x,y]\}\), \(d(x,x)=0\). The pair \(([0,\lambda), d_{f})\) is called a \(\gamma-\)comb defined by \(f\). We show that each cellular ordinal ballean can be represented as a \(\gamma-\)comb. In General Asymptology, cellular ordinal balleans play a part of ultrametric spaces. Lugansk National Taras Shevchenko University 2016-07-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/200 Algebra and Discrete Mathematics; Vol 21, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/200/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/200/73 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/200/74 Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
ultrametric space cellular ballean ordinal ballean \((\lambda,\gamma)-\)comb 54A05 54E15 54E30 |
| spellingShingle |
ultrametric space cellular ballean ordinal ballean \((\lambda,\gamma)-\)comb 54A05 54E15 54E30 Protasov, Igor Protasova, Ksenia The comb-like representations of cellular ordinal balleans |
| topic_facet |
ultrametric space cellular ballean ordinal ballean \((\lambda,\gamma)-\)comb 54A05 54E15 54E30 |
| format |
Article |
| author |
Protasov, Igor Protasova, Ksenia |
| author_facet |
Protasov, Igor Protasova, Ksenia |
| author_sort |
Protasov, Igor |
| title |
The comb-like representations of cellular ordinal balleans |
| title_short |
The comb-like representations of cellular ordinal balleans |
| title_full |
The comb-like representations of cellular ordinal balleans |
| title_fullStr |
The comb-like representations of cellular ordinal balleans |
| title_full_unstemmed |
The comb-like representations of cellular ordinal balleans |
| title_sort |
comb-like representations of cellular ordinal balleans |
| description |
Given two ordinal \(\lambda\) and \(\gamma\), let \(f:[0,\lambda) \rightarrow [0,\gamma)\) be a function such that, for each \(\alpha<\gamma\), \(\sup\{f(t): t\in[0, \alpha]\}<\gamma.\) We define a mapping \(d_{f}: [0,\lambda)\times [0,\lambda) \longrightarrow [0,\gamma)\) by the rule: if \(x<y\) then \(d_{f}(x,y)= d_{f}(y,x)= \sup\{f(t): t\in(x,y]\}\), \(d(x,x)=0\). The pair \(([0,\lambda), d_{f})\) is called a \(\gamma-\)comb defined by \(f\). We show that each cellular ordinal ballean can be represented as a \(\gamma-\)comb. In General Asymptology, cellular ordinal balleans play a part of ultrametric spaces. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/200 |
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