I have a question which may be naive but I can not find the answer in general reference about Skorokhod topology.
Let $\{w_n\}_{n\ge 0}$ be a sequence of cadlag functions defined on $[0,1]$ such that
$$\lim_{n\to\infty}\rho(w_n,w_0)=0,$$
where $\rho$ denotes the Skorokhod distance. Then we know that there exists a countable set $T\subseteq [0,1]$ such that
$$\lim_{n\to\infty}w_n(t)=w_0(t),~ \forall t\in [0,1]\backslash T$$
My question is if one has
$$\lim_{n\to\infty}\rho(w_n,v_n)=0$$
then one can also find a countable set $T\subseteq [0,1]$ such that
$$\lim_{n\to\infty}(w_n(t)-v_n(t))=0,~ \forall t\in [0,1]\backslash T$$
Many thx for the reply!