2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105048A Gauss equation is proved for subspaces of Alexandrov spaces of curvature bounded above by K. That is, a subspace of extrinsic curvature less than or equal to A, defined by a cubic inequality on the difference of arc and chord, has intrinsic curvature less than or equal to K+A^2. Sharp bounds on injectivity radii of subspaces, new even in the Riemannian case, are derived.17 pages, 4 figuresDifferential GeometryMetric Geometry53C70,53C20,53B25text