2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139399We show that rough isometries between metric spaces X, Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough isometries between X and Y can be reconstructed from structurally enriched rough isometries between their Lipschitz function spaces.21 pages, 3 figuresMetric Geometry26A16 (Primary); 41A30, 06B30 (Secondary)text