$P\_n[0,1]$ be the set of all polynomial of degree atmost $n$ with supnorm is it a closed in $C[0,1]$? and $P[0,1]$ is set of all polynomials in $C[0,1]$ I know which is dense in $C[0,1]$ as we know by Weirstrass Polynomial approximation theorem any continous function can be uniformly approximated by sequence of polynomials. 

Thank you for help.