  We consider the transformation $\ev$ which associates to any element in a
K-algebra A a function on the the set of its K-points. This is the analogue of
the fundamental Gelfand transform. Both $\ev$ and its dual $\ev^*$ are the maps
from a discrete K-module to a topological K-module and we investigate in which
case the image of each map is dense. The answer is nontrivial for various
choices of K and A already for A=K[x], the polynomial ring in one variable.
Applications to the structure of algebras of cohomology operations are given.
