Boundary of Empty Set is Empty/Proof 2

Theorem

Let $T$ be a topological space.

Then:

$\partial_T \O = \O$

where $\partial_T \O$ denotes the boundary in topology $T$ of $\O$.

Proof

From Open and Closed Sets in Topological Space, $\O$ is clopen in $T$.

The result follows from Set is Clopen iff Boundary is Empty.

$\blacksquare$