  We develop the theory of invariant structure preserving and free functions on
a general structured topological space. We show that an invariant structure
preserving function is pointwise approximiable by the appropriate analog of
polynomials in the strong topology and therefore a free function. Moreover, if
a domain of operators on a Hilbert space is polynomially convex, the set of
free functions satisfies a Oka-Weil Kaplansky density type theorem --
contractive functions can be approximated by contractive polynomials.
