Can this set becomes a Banach space?

Question

Given a set $B=\{x | x:[t_0, T]\rightarrow \mathbb{R}^n,$ $x$ is a differentiable function on $[t_0, T]-\{t_1,...,t_M\}$ and $x(t^{+}_k)=\lim \limits_{t \rightarrow t^{+}_k} x(t)$ and $x(t^{-}_k)=\lim \limits_{t \rightarrow t^{-}_k} x(t)$ exists with the condition $x(t^{-}_k)=x(t_k)$ and $x(t_0)=\lim \limits_{t\rightarrow t^{-}_0}x(t)\}.$ Then my question is whether $B$ is a banach space on real field? Further whether it means all differentiable functions on $[t_0, T]$ will be included in $B?$