Automatic continuity of group homomorphisms

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.

CONTINUITY IN FUNDAMENTAL LOCALLY MULTIPLICATIVE TOPOLOGICAL ALGEBRAS

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

Automatic Continuity of Homomorphisms and Fixed Points on Metric Compacta

We prove that arbitrary homomorphisms from one of the groups Homeo(2), Homeo(2), Aut(Q, <), Homeo(R) or Homeo(S) into a separable group are automatically continuous. This has consequences for the representations of these groups as discrete groups. For example, it follows, in combination with a result of V. G. Pestov, that any action of the discrete group Homeo+(R) by homeomorphisms on a compact...

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.