2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228071Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.This is the version published by Algebraic & Geometric Topology on 20 September 2006Geometric Topology57M27, 57N10text