Automatic continuity and representation of group homomorphisms defined between groups of continuous functions

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Automatic continuity of group homomorphisms

We survey various aspects of the problem of automatic continuity of homomorphisms between Polish groups.

Separate and Joint Continuity of Homomorphisms Defined on Topological Groups

In this paper we prove the following theorem. “Let H be a countably Čech–complete topological group, X be a topological space and (G, ·, τ) be a topological group. If f : H ×X → G is a separately continuous mapping with the property that for each x ∈ X, the mapping h 7→ f(h, x) is a group homomorphism, then for each q–point x0 ∈ X the mapping f is jointly continuous at each point of H ×{x0}.” W...

automatic continuity of homomorphisms between banach algebras and frechet algebras

Automatic continuity of surjective $n$-homomorphisms on Banach algebras

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.