McShane-Whitney Pairs

We present a constructive version of the classical McShane-Whitney theorem on the extendability of real-valued Lipschitz functions defined on a subset of a metric space. Through the introduced notion of a McShane-Whitney pair we study some abstract properties of this extension theorem showing how the behavior of a Lipschitz function defined on the subspace of the pair affect its McShane-Whitney extensions on the space of the pair. As a consequence, a Lipschitz version of the theory around the Hahn-Banach theorem is formed. We work within Bishop’s informal system of constructive mathematics .