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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 415, Pages 75–90 (Mi znsl5687)  
This article is cited in 1 scientific paper (total in 1 paper)

Pretrees and arborescent convexities

A. V. Malyutin

St. Petersburg Department of Steklov Institute of Mathematics RAN, Fontanka 27, 191023 St. Petersburg, Russia
Full-text PDF (241 kB) Citations (1)
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Abstract: We prove that the class of pretrees, the theory of which is developed by L. Ward [11], B. Bowditch [2], S. Adeleke and P. Neumann [1], and others, is canonically isomorphic to the class of arborescent convexity spaces introduced by P. Duchet [6] in the framework of abstract convexity theory.
Key words and phrases: tree, pretree, dendritic, arborescent, betweenness, convexity, Carathéodory number, variety, interval space.
Received: 06.05.2013
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 212, Issue 5, Pages 566–576
DOI: https://doi.org/10.1007/s10958-016-2689-1
Bibliographic databases:
Document Type: Article
UDC: 514.17+519.172.1
Language: English
Citation: A. V. Malyutin, “Pretrees and arborescent convexities”, Geometry and topology. Part 12, Zap. Nauchn. Sem. POMI, 415, POMI, St. Petersburg, 2013, 75–90; J. Math. Sci. (N. Y.), 212:5 (2016), 566–576
Citation in format AMSBIB
\Bibitem{Mal13}
\by A.~V.~Malyutin
\paper Pretrees and arborescent convexities
\inbook Geometry and topology. Part~12
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 415
\pages 75--90
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5687}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 212
\issue 5
\pages 566--576
\crossref{https://doi.org/10.1007/s10958-016-2689-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953410564}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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