  When 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
Fr\'echet 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.
