# Bohr topology and difference sets for some abelian groups

@article{Griesmer2016BohrTA, title={Bohr topology and difference sets for some abelian groups}, author={John T. Griesmer}, journal={arXiv: Dynamical Systems}, year={2016} }

For a fixed prime $p$, $\mathbb F_{p}$ denotes the field with $p$ elements, and $\mathbb F_{p}^{\omega}$ denotes the countable direct sum $\bigoplus_{n=1}^{\infty} \mathbb F_{p}$. Viewing $\mathbb F_{p}^{\omega}$ as a countable abelian group, we construct a set $A\subseteq \mathbb F_{p}^{\omega}$ having positive upper Banach density while the difference set $A-A:=\{a-b:a,b\in A\}$ does not contain a Bohr neighborhood of any $c\in \mathbb F_{p}^{\omega}$. For $p=2$ we obtain a stronger…

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