  In 1978, Dales posed a question about the uniqueness of the (F)-algebra
topology for (F)-algebras of power series in k indeterminates. We settle this
in the affirmative for Frechet algebras of power series in k indeterminates.
The proof goes via first completely characterizing these algebras; in
particular, it is shown that the Beurling-Frechet algebras of semiweight type
do not satisfy a certain equicontinuity condition due to Loy. Some applications
to the theory of automatic continuity are also given, in particular the case of
Frechet algebras of power series in infinitely many indeterminates.
