2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145034We give a new proof of a theorem by Le Gall & Paulin, showing that scaling limits of random planar quadrangulations are homeomorphic to the 2-sphere. The main geometric tool is a reinforcement of the notion of Gromov-Hausdorff convergence, called 1-regular convergence, that preserves topological properties of metric surfaces.11pp, 1 figureProbability60C05 ; 60F05 ; 60D05On the sphericity of scaling limits of random planar quadrangulationstext