RESEARCH ANNOUNCEMENTS The Uniqueness of Topology and Continuity of Systems of Derivations on Locally Convex F-Algebras(*)

The uniqueness of topology is an important problem in the theory of auto-matic continuity.In 1967,Johnson proved the famous uniqueness theorem of normwhich asserts that any Jacobson semisimple Bauach algebra has the unique com-plete norm topology.Carpenter proved this for commutative Frechet algebras.In1976,Esterle proved that a Jacobson semisimple Banach algebra has the unique-topology as an F-algebra.A main result we obtained here was that a Jacobsonsemisimple locally convex F—algebra whose maximal regular right ideals are clo-sed has the unique topology as an F—algebra.