Empty Set is Element of Topology

Theorem
Let $T = \struct {X, \tau}$ be a topological space.

Then the empty set $\O$ is an open set of $T$.

Proof
By Empty Set is Subset of All Sets:
 * $\O \subseteq \tau$

By Union of Empty Set:
 * $\ds \O = \bigcup \O$

By :
 * $\O \in \tau$