Is $F=\left\lbrace f: f\in C_{\left[0, 1\right]}, f\left(0\right)=f\left(1\right)\right\rbrace$ complete metric space?
I know how to prove that $C_{\left[0, 1\right]}$ is complete. But I don't know how to use condition that $f\left(0\right)=f\left(1\right)$.