The comb-like representations of cellular ordinal balleans
Given two ordinal λ and γ, let f:[0,λ)→[0,γ) be a function such that, for each α<γ, sup{f(t):t∈[0,α]}<γ. We define a mapping df:[0,λ)×[0,λ)⟶[0,γ) by the rule: if x<y then df(x,y)=df(y,x)=sup{f(t):t∈(x,y]}, d(x,x)=0. The pair ([0,λ),df) is called a γ−comb defined by f. We show that each cel...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2016 |
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| Language: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155256 |
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| Cite this: | The comb-like representations of cellular ordinal balleans / I. Protasov, K. Protasova // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 282-286. — Бібліогр.: 8 назв. — англ. |
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Protasov, I. Protasova, K. 2019-06-16T14:51:28Z 2019-06-16T14:51:28Z 2016 The comb-like representations of cellular ordinal balleans / I. Protasov, K. Protasova // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 282-286. — Бібліогр.: 8 назв. — англ. 1726-3255 2010 MSC:54A05, 54E15, 54E30. https://nasplib.isofts.kiev.ua/handle/123456789/155256 Given two ordinal λ and γ, let f:[0,λ)→[0,γ) be a function such that, for each α<γ, sup{f(t):t∈[0,α]}<γ. We define a mapping df:[0,λ)×[0,λ)⟶[0,γ) by the rule: if x<y then df(x,y)=df(y,x)=sup{f(t):t∈(x,y]}, d(x,x)=0. The pair ([0,λ),df) is called a γ−comb defined by f. We show that each cellular ordinal ballean can be represented as a γ−comb. In General Asymptology, cellular ordinal balleans play a part of ultrametric spaces. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The comb-like representations of cellular ordinal balleans Article published earlier |
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| title |
The comb-like representations of cellular ordinal balleans |
| spellingShingle |
The comb-like representations of cellular ordinal balleans Protasov, I. Protasova, K. |
| 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 |
| author |
Protasov, I. Protasova, K. |
| author_facet |
Protasov, I. Protasova, K. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
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Інститут прикладної математики і механіки НАН України |
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Article |
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Given two ordinal λ and γ, let f:[0,λ)→[0,γ) be a function such that, for each α<γ, sup{f(t):t∈[0,α]}<γ. We define a mapping df:[0,λ)×[0,λ)⟶[0,γ) by the rule: if x<y then df(x,y)=df(y,x)=sup{f(t):t∈(x,y]}, d(x,x)=0. The pair ([0,λ),df) is called a γ−comb defined by f. We show that each cellular ordinal ballean can be represented as a γ−comb. In General Asymptology, cellular ordinal balleans play a part of ultrametric spaces.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155256 |
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| citation_txt |
The comb-like representations of cellular ordinal balleans / I. Protasov, K. Protasova // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 282-286. — Бібліогр.: 8 назв. — англ. |
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2025-11-24T09:18:50Z |
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2025-11-24T09:18:50Z |
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