On extending characters

Milnes, Paul

doi:10.1090/S0002-9939-1981-0609650-9

On extending characters
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Proc. Amer. Math. Soc. 82 (1981), 196-198 Request permission

Abstract:

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

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