(a) Show that in a Hausdorff topological space any compact set is closed.\\
(b) If $\left( X , d _ { 1 } \right)$ and $\left( Y , d _ { 2 } \right)$ are two metric spaces that are homeomorphic then does completeness of $\left( X , d _ { 1 } \right)$ imply the completeness of $\left( Y , d _ { 2 } \right)$? Give reasons for your answer.