  It is shown that if $A$ is a uniform algebra generated by real-analytic
functions on a suitable compact subset $K$ of a real-analytic variety such that
the maximal ideal space of $A$ is $K$, and every continuous function on $K$ is
locally a uniform limit of functions in $A$, then $A=C(K)$. This gives an
affirmative answer to a special case of a question from the Proceedings of the
Symposium on Function Algebras held at Tulane University in 1965.
