2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60871It is shown that a smooth n dimensional manifold with a boundary in R^n admits a Boolean representation in terms of closed half spaces defined by the tangent hyperplanes at the points on its boundary. A similar result is established for smooth functions on closed convex domains in R^n. The latter result is considered as a form of the Legendre transformation.6 pages, 1 figureClassical Analysis and ODEs26B40; 26B25text