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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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Інститут прикладної математики і механіки НАН України
2016
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/155256 |
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irk-123456789-1552562019-06-17T01:28:23Z The comb-like representations of cellular ordinal balleans Protasov, I. Protasova, K. 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. 2016 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/155256 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| description |
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. |
| format |
Article |
| author |
Protasov, I. Protasova, K. |
| spellingShingle |
Protasov, I. Protasova, K. The comb-like representations of cellular ordinal balleans Algebra and Discrete Mathematics |
| author_facet |
Protasov, I. Protasova, K. |
| author_sort |
Protasov, I. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155256 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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AT protasovi thecomblikerepresentationsofcellularordinalballeans AT protasovak thecomblikerepresentationsofcellularordinalballeans AT protasovi comblikerepresentationsofcellularordinalballeans AT protasovak comblikerepresentationsofcellularordinalballeans |
| first_indexed |
2023-05-20T17:46:28Z |
| last_indexed |
2023-05-20T17:46:28Z |
| _version_ |
1796154061111689216 |