On Perfectness in Topological Algebras

Some topological algebras can be represented as the projective limit of a projective system of algebras of some type. This is the case of complete m-convex algebras and their Arens-Michael decomposition. In this paper we study the notion of perfectness applied to a topological algebra and prove that all complete m-pseudoconvex algebras are perfect. We also prove that this property is preserved under finite products.