Remark that a uniform weak null set $A$ of $c_0$ satisfied that for any $\epsilon>0$ there exists a positive number $N(\epsilon)$ such that for every $f$ in $B(\ell_1)$, the unit ball of the space $\ell_1$，we have that the number of $a$ in $A$ where $|f(a)|>\epsilon$ is not larger than $N(\epsilon)$.
A uniformly embedding mapping $f$ from the metric space $X$ to $Y$ satisfied that $f$ and $f^{-1}$ are both uniformly continuous.
