Closure of Empty Set is Empty Set

Theorem

Let $T = \left({S, \tau}\right)$ be a topological space.

Then the closure of the empty set $\varnothing$ in $T$ is $\varnothing$.

Proof

From Empty Set is Closed in Topological Space, $\varnothing$ is closed in $T$.

The result follows from Closed Set equals its Closure.

$\blacksquare$