Let $Y$ be a subspace of a topological space $(X, T)$. Prove that if $A$ is a closed subset of $Y$ and $Y$ is a closed subset in $X$ then $A$ is a closed subset of $X$
My attempt: Since $Y$ is a subspace of $X$, the open sets are of the form $Y\cap U$ with $U\in T$ and $Y$ is closed in $X$ implies that $X-Y$ is open and $A$ is closed in $Y$ implies $Y-A$ is open.
I am really stuck at this point. Can someone please help.
