Empty Set is Open and Closed in Metric Space

Theorem
Let $M = \left({A, d}\right)$ be a metric space.

Then the empty set $\varnothing$ is both open and closed in $M$.

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

From Empty Set is Closed in Metric Space, $\varnothing$ is closed in $M$.