On extending characters

Abstract

Amplifying modestly on recent work of R. W. Henrichs, we indicate that, while the impossibility of extending a continuous character ψ \psi on a subgroup H H of a topological group G G to a character on G G is often due to algebraic problems, the impossibility of extending ψ \psi to a continuous positive definite function on G G can often be viewed as a problem with uniform continuity.