Hausdorff-space/Compact subset/Closed/Fact/Proof/Exercise

Let ${\displaystyle {}X}$ be a Hausdorff space, and let ${\displaystyle {}Y\subseteq X}$ be a subset that carries the induced topology. Let ${\displaystyle {}Y}$ be compact. Show that ${\displaystyle {}Y}$ is closed in ${\displaystyle {}X}$.