Lydia Dorothea Außenhofer

Reflexive group topologies on $\mathbb{Z}$ .

A strictly increasing sequence ${\bf b}=(b_n)_{n\in {\mathbb N}_0}$ of natural numbers is called a $D$ -sequence, if $b_0=1$ and if $b_n$ divides $b_{n+1}$ for every $n\in\mathbb N$ . There exists a finest group topology $T_{{\bf b}}$ on $\mathbb Z$ in which $(b_n)$ converges to $0$ . We characterize those $D$ -sequences ${\bf b}$ in $\mathbb Z$ for which $(\mathbb Z,T_{{\bf b}})$ is reflexive and show that for every $D$ -sequence ${\bf b}$ the character group of $(\mathbb Z,T_{{\bf b}})$ is reflexive.