Remarques sur un article de Israel Aharoni sur les prolongements lipschitziens dansc ₀

Abstract

We give a purely metric proof of the following result: let (X,d) be a separable metric space; for all ɛ>0 there is an injectionf ofX inC ⁺₀ such that:

$$\forall x,y \in X,d(x, y) \leqq \parallel f(x) - f(y)\parallel _\infty \leqq (3 + \varepsilon )d(x, y).$$

It is a more precise version of a result of I. Aharoni. We extend it to metric space of cardinal α⁺ (for infinite α).