Union of Interiors and Boundary Equals Whole Space

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

Let $A$ be a subset of $T$.

Then:
 * $S = \Int A \cup \partial A \cup \Int {A'}$

where:
 * $A' = S \setminus A$ denotes the complement of $A$ relative to $S$
 * $\Int A$ denotes the interior of $A$
 * $\partial A$ denotes the boundary of $A$.