Discretely normed Abelian groups
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A discrete norm on an Abelian groupA is a non-negative function ‖ · ‖A → ℝ which satisfies the triangle inequality, is homogenous with respect to scaling ofA by ℤ and is bounded away from 0 onA/{0}.A countable Abelian group is discretely normed if and only if the group is free.
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