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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| Date: | 2016 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2016
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/200 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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. |
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