  The uniform disconnectedness is an important invariant property under
bi-Lipschitz mapping, and the Assouad dimension $\dim _{A}X<1$ implies the
uniform disconnectedness of $X$. According to quasi-Lipschitz mapping, we
introduce the quasi-Assouad dimension $\dim _{qA}$ such that $\dim _{qA}X<1$
implies its quasi uniform disconnectedness. We obtain $\overline{\dim }
_{B}X\leq \dim _{qA}X\leq \dim _{A}X$ and compute the quasi-Assouad dimension
of Moran set.
