Automatic continuity for the unitary group

TL;DR

This paper proves that any group homomorphism from the infinite-dimensional unitary or orthogonal group to a separable group must be continuous, establishing a significant continuity property for these infinite-dimensional groups.

Contribution

It demonstrates automatic continuity of homomorphisms from infinite-dimensional unitary and orthogonal groups to separable groups, a novel result in topological group theory.

Findings

Homomorphisms are automatically continuous

Infinite-dimensional unitary and orthogonal groups have this property

Supports the structure theory of infinite-dimensional groups

Abstract

We show that every homomorphism from the infinite-dimensional unitary or orthogonal group to a separable group is continuous.