2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100172We study a new bi-Lipschitz invariant λ(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor controlled by λ(M). We prove that λ(M) is finite for several important classes of metric spaces. These include metric trees of arbitrary cardinality, groups of polynomial growth, Gromov-hyperbolic groups, certain classes of Riemannian manifolds of bounded geometry and finite direct sums of arbitrary combinations of these objects. On the other hand we construct an example of a two-dimensional Riemannian manifold M of bounded geometry for which λ(M)=\infty.Several new results are added, some important estimates are improvedMetric GeometryFunctional Analysis26B35; 54E35; 46B15text