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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Metrizable and $\mathbb R$-metrizable betweenness spaces


Author: Juraj Simko
Journal: Proc. Amer. Math. Soc. 127 (1999), 323-325
MSC (1991): Primary 03B30, 03C52, 51F99
MathSciNet review: 1458264
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Abstract: It is proved that the theory of the class of all betweenness spaces metrizable by real-valued metrics does not coincide with the theory of the class of all betweenness spaces metrizable by metrics taking values in any ordered field. This solves a problem raised by Mendris and Zlato\v{s}.


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Additional Information

Juraj Simko
Affiliation: Department of Mathematics, Faculty of Chemical Technology, Slovak Technical University, 81237 Bratislava, Slovakia
Email: simko@cvt.stuba.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04515-3
PII: S 0002-9939(99)04515-3
Keywords: Betweenness relation, metric, ordered field, elementary class
Received by editor(s): April 2, 1997
Received by editor(s) in revised form: May 15, 1997
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 1999 American Mathematical Society