Automatic Continuity for Homomorphisms into Free Products

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.

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 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.