Isometries in ordered groups
Jiří Rachůnek · Czechoslovak Mathematical Journal · 1984
In [6], K. L. N. Swamy describes geometric properties of the commutative latticeordered groups autometrized by means of the absolute values of their elements.The isometrics of lattice-ordered groups are studied by K. L. N. Swamy in [7], [8], [9] for the commutative case and by J. Jakubik in [4], [5] for the general case.In this paper the notions of the autometry and isometry are generalized to any ordered groups and studied for the class of 2-isolated Riesz groups in particular.We use the terminology and notation from the books [l] and [3] (in the additive form).