  Let A and B be commutative locally convex algebras with unit. A is assumed to
be a uniform topological algebra. Let h be an injective homomorphism from A to
B. Under additional assumptions, we characterize the continuity of the
homomorphism h^(-1) / Im(h) by the fact that the radical (or strong radical) of
the closure of Im(h) has only zero as a common point with Im(h). This gives an
answer to a conjecture concerning some automatic continuity theorems on uniform
topological algebras.
