2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78421Let H be the supremum of finitely many real polynomials of degree d and assume that H has a strict local minimum at 0. We prove a Łojasiewicz-type inequality $H(x_1,...,x_n) > ||(x_1,...,x_n)||^s$ where s depends only on d and n. This implies a similar inequality where $(x_1,...,x_n)$ runs through the points of a semi-algebraic set.LATEX2e, 9 pagesAlgebraic Geometrytext