Boundary of Empty Set is Empty/Proof 1

Proof
By Boundary is Intersection of Closure with Closure of Complement:
 * $\partial_T \varnothing = \varnothing^- \cap \complement_T \left({\varnothing}\right)^-$

where $\varnothing^-$ denotes the closure of $\varnothing$.

By Closure of Empty Set is Empty Set:
 * $\varnothing^- = \varnothing$

Thus the result follows by Intersection with Empty Set.