2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71591This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embedings into l_p, and the particular case of the hypercube.36 pages, 0 figures. To appear in Advances in MathematicsMetric Geometrytext