Metric Space is Closed in Itself

Theorem
Let $M = \struct {A, d}$ be a metric space.

Then $A$ is closed in $M$.

Proof
From Empty Set is Open in Metric Space, $\O$ is open in $M$.

But:
 * $A = \relcomp A \O$

where $\complement_A$ denotes the set complement relative to $A$.

The result follows by definition of closed set.