# Is the closure of a closable projection continuous?

Let $$X$$ be a Banach Space and let $$P$$ be a densely defined operator on $$X$$ such that

$$P$$ is closable

$$R(P)\subset D\left( P\right)$$ and $$P^{2}=P$$

Is $$\overline{P}$$ an everywhere defined continuous projection ?

Thank you