About a definition of metric over an abelian linearly ordered group

Bice Cavallo, Livia D’Apuzzo

Abstract


A G-metric over an abelian linearly ordered group G = (G,⊙,≤) is a binary operation, d G , verifying suitable properties. We consider a particular G metric derived by the group operation ⊙ and the total weak order ≤, and show that it provides a base for the order topology associated to G.


Keywords


G-metric, abelian linearly ordered group, multi-criteria decision making.

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.