# A subspace of Banach space is complete if and only if it is closed.

"A subspace $Y$ of Banach space $X$ is complete if and only if $Y$ is closed in $X$"
from left to right "let $X$ is Banach space, $Y\subset X$. so, $Y$ is Banach space. consider of Banach space definition, every Cauchy sequence of $Y$ is converge to $x\in X$ then $Y$ is closed on $X$".