The uniform disconnectedness is an important invariant property under
bi-Lipschitz mapping, and the Assouad dimension dimAX<1 implies the
uniform disconnectedness of X. According to quasi-Lipschitz mapping, we
introduce the quasi-Assouad dimension dimqA such that dimqAX<1
implies its quasi uniform disconnectedness. We obtain dimBX≤dimqAX≤dimAX and compute the quasi-Assouad dimension
of Moran set