Element-wise description of the $\mathcal{I}$-characterized subgroups of the circle

Raffaele Di Santo, Dikran Dikranjan, Anna Giordano Bruno +1

According to Cartan, given an ideal $\mathcal{I}$ of $\mathbb{N}$, a sequence $(x_n{)}_{n\in \mathbb{N}}$ in the circle group $\mathbb{T}$ is said to {\em $\mathcal{I}$-converge} to a poin…