A note on the BMO-Teichmüller space

Astala–Zinsmeister [2] introduced a new topology on the set of all strongly quasisymmetric homeomorphisms of the unit circle denoted by SQS(S1)SQS(S1) by means of BMO norm. Under this new topology, we prove that SQS(S1)SQS(S1) is a partial topological group, and the characteristic topological subgroup of SQS(S1)SQS(S1) consists of strongly symmetric homeomorphisms.