2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152353When dealing with concrete problems in a function space on R^n, it is sometimes helpful to have a dense subspace consisting of functions of a particular type, adapted to the problem under consideration. We give a theorem that allows one to write down many of such subspaces in commonly occurring Fréchet function spaces. These subspaces are all of the form $\{pf_0 | p\in{\cal P}\}$ where $f_0$ is a fixed function and ${\cal P}$ is an algebra of functions. Classical results like the Stone-Weierstrass theorem for polynomials and the completeness of the Hermite functions are related by this theorem.14 pages, no figures, plain TexFunctional Analysistext