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 Algebra Discrete Math., 2016, Volume 21, Issue 2, Pages 282–286 (Mi adm568)  RESEARCH ARTICLE

The comb-like representations of cellular ordinal balleans

Igor Protasov, Ksenia Protasova

Taras Shevchenko National University of Kyiv, Department of Cybernetics, Volodymyrska 64, 01033, Kyiv Ukraine

Abstract: 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.

Keywords: ultrametric space, cellular ballean, ordinal ballean, $(\lambda,\gamma)$-comb. Full text: PDF file (279 kB) References: PDF file   HTML file

Bibliographic databases:  MSC: 54A05, 54E15, 54E30
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Citation: Igor Protasov, Ksenia Protasova, “The comb-like representations of cellular ordinal balleans”, Algebra Discrete Math., 21:2 (2016), 282–286 Citation in format AMSBIB
\Bibitem{ProPro16}
\by Igor~Protasov, Ksenia~Protasova
\paper The comb-like representations of cellular ordinal balleans
\jour Algebra Discrete Math.
\yr 2016
\vol 21
\issue 2
\pages 282--286
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3537451}

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This publication is cited in the following articles:
1. T. Banakh, I. Protasov, D. Repovs, S. Slobodianiuk, “Classifying homogeneous cellular ordinal balleans up to coarse equivalence”, Colloq. Math., 149:2 (2017), 211–224     2. A. Lambert, G. Uribe Bravo, “The comb representation of compact ultrametric spaces”, P-Adic Numbers Ultrametric Anal. Appl., 9:1 (2017), 22–38     • Number of views: This page: 80 Full text: 17 References: 31 Contact us: math-net2019_10 [at] mi-ras ru Terms of Use Registration Logotypes © Steklov Mathematical Institute RAS, 2019