  A recent paper by Polterovich, Shalom and Shem-Tov has shown that
non-discrete, conjugation invariant norms on arithmetic Chevalley groups of
higher rank give rise to very restricted topologies. Namely, such topologies
always have profinite norm-completions. In this note, we sketch an argument
showing that this also holds for ${\rm SL}_2(R)$ for $R$ a ring of algebraic
integers with infinitely many units.
