Abstract
The p-adic completion ℚp of the rational numbers induces a different absolute value |⋅|p than the typical | ⋅| we have on the real numbers. In this paper we compare and contrast functions f : ℝ+ → ℝ+, for which the composition with the p-adic metric dp generated by |⋅|p is still a metric on ℚp, with the usual metric preserving functions and the functions that preserve the Euclidean metric on ℝ. In particular, it is shown that f ∘ dp is still an ultrametric on ℚp if and only if there is a function g such that f ∘ dp = g ∘ dp and g ∘ d is still an ultrametric for every ultrametric d. Some general variants of the last statement are also proved.
(Communicated by David Buhagiar )
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