Automatic continuity of homomorphisms between topological semigroups

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

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.

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.

Automatic continuity for homomorphisms into free products

A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In particular, any completely metrizable group topology on a free product is discrete.