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Betweenness spaces and tree algebras. (English) Zbl 0616.05031
It is proved that tree algebras in the sense of L. Nebeský [see B. Zelinka, Cas. Pestovani Mat. 107, 59-68 (1982; Zbl 0487.05022)] and, hence, trees themselves, may be regarded as betweenness spaces of certain kind. In terms of betweenness relation trees have been characterized already by M. Sholander [Proc. Am. Math. Soc. 3, 369-381 (1952; Zbl 0047.054)]; our axiom system is somewhat simpler than his one.
MSC:
05C05 Trees
08A02 Relational systems, laws of composition
06A99 Ordered sets
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