Extensions of Lipschitz functions and Grothendieck s bounded approximation property
A metric compact space M is seen as the closure of the union of a sequence (Mn) of finite n dense subsets. Extending to M (up to a vanishing uniform distance) Banach space valued Lipschitz functions defined on Mn, or defining linear continuous near extension operators for real valued Lipschitz functions on Mn, uniformly on n is shown to be equivalent to the bounded approximation property for the Lipschitz free space F (M) over M. Several consequences are spelled out.