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The amalgamation property for $ G$-metric spaces


Author: H. H. Hung
Journal: Proc. Amer. Math. Soc. 37 (1973), 53-58
MSC: Primary 54E35; Secondary 06A60
DOI: https://doi.org/10.1090/S0002-9939-1973-0314008-1
MathSciNet review: 0314008
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Abstract: Let G be a (totally) ordered (abelian) group. A G-metric space $ (X,\rho )$ consists of a nonempty set X and a G-metric $ \rho :X \times X \to G$ (satisfying the usual axioms of a metric, with G replacing the ordered group of real numbers). That the amalgamation property holds for the class of all metric spaces is attributed, by Morley and Vaught, to Sierpiński. The following theorem is proved. Theorem. The class of all G-metric spaces has the amalgamation property if, and only if, G is either the ordered group of the integers or the ordered group of the reals.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0314008-1
Keywords: Amalgamation property, relational systems, totally ordered abelian groups, order completeness, Dedekind cuts, G-metric spaces
Article copyright: © Copyright 1973 American Mathematical Society

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