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

This article is cited in 2 scientific papers (total in 2 papers)

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.

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Bibliographic databases:
MSC: 54A05, 54E15, 54E30
Received: 29.01.2016
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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
\mathnet{http://mi.mathnet.ru/adm568}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3537451}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000382847700009}


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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  mathscinet  zmath  isi  scopus
    2. A. Lambert, G. Uribe Bravo, “The comb representation of compact ultrametric spaces”, P-Adic Numbers Ultrametric Anal. Appl., 9:1 (2017), 22–38  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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