In this note, a topological
algebra A is an algebra over the field of complex numbers together with a Hausdorff
locally convex topology which makes multiplication jointly continuous. A is called
B-complete (Br-complete) if every continuous (continuous, one-to-one) and almost
open algebra homomorphism from A onto any topological algebra is open.
For a completely regular space X, C(X) is the algebra of all continuous
complex-valued functions with the usual pointwise operations and the compact-open
topology. The main theorem states that C(X) is a B-complete algebra iff X is a
k-space.
