Let $E:=c\_{00}$. Recall that$$c\_{00}:=\{(x\_n)\_{n\in \mathbb{N}}|\exists M\geq 0\,:\,(x\_n)\_{n\in \mathbb{N}}=(x\_1,x\_2,\ldots ,x\_M,0,0,0,0,\ldots )\}.$$We are equipping this with the topology given by norm$$\|(x\_n)\|\_\infty :=\sup \{|x\_n|:n\in \mathbb{N}\}.$$
Is $c\_{00}$ closed?