Let $(X,d)$ be a metric space.
a)$\emptyset$ is open in $X$
b)$\emptyset$ is closed in $X$
a) By the definition of open set we have $A\in X$ is open if $B(x,\epsilon)\subset A$ for $x\in X$.The $\emptyset$ is open because a ball centred in the $\emptyset$ is contained in the set itself.
How do I prove b)? Is my proof of $A$ right?
Is the $\emptyset$ opened and closed? I am confused on this issue.