Let $X$ be a metric space and $Y\subset X$ a subspace of $X.$
I have to prove the statement:
(a) Prove that if $X$ is complete and $Y$ is closed, then $Y$ is complete.
(b) Prove that if $Y$ is complete then $Y$is closed in $X$.
I'm following the definition (Complete metric spaces). A metric space is called complete if every Cauchy sequence in the space converges.
But, I am confused how to start to prove....