Empty Set is Closed/Normed Vector Space

Theorem
Let $M = \struct {X, \norm {\, \cdot \,}}$ be a normed vector space.

Then the empty set $\O$ is closed in $M$.

Proof
From Normed Vector Space is Open in Itself, $X$ is open in $M$.

But:
 * $\varnothing = \map {\complement_X} X$

where $\complement_X$ denotes the set complement relative to $X$.

The result follows by definition of closed set.