1
$\begingroup$

Let $(G,\mathcal T)$ be an infinite Hausdorff precompact abelian topological group and let $G$ have exponent $p$ where $p$ is a prime number.

Can it be proved that there are at least $p+1$ continuous homomorphisms $f:G\to \Bbb T$, where $\Bbb T$ is the circle group?

$\endgroup$
1
$\begingroup$

By Proposition 3.4 of

D. Dikranjan; L. Stoyanov. An elementary approach to Haar integration and Pontryagin duality in locally compact abelian groups. Topology Appl. 158 (2011), no. 15, 1942--1961.

if $G$ is an infinite abelian group and $\mathcal T$ is a Hausdorff precompact group topology on $G$, there are infinitely many continuous homomorphisms $f:G\to \Bbb T$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.