Injective Subsets of $l_{\infty}(I)$

Abstract

We give an explicit characterization of all injective subsets of the model space $l_{\infty}(I)$ for a general set $I$, in terms of inequalities involving $1$-Lipschitz functions. Since the class of all injective metric spaces coincides with the one of all absolute $1$-Lipschitz retracts, the present work yields a characterization of all the subsets of $l_{\infty}(I)$ that are absolute $1$-Lipschitz retracts.