The comb-like representations of cellular ordinal balleans

• Published in: Algebra and Discrete Mathematics
• Date: 2016
• Main Authors: Protasov, I., Protasova, K.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155256
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• 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.

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...