Set is Clopen iff Boundary is Empty
(Redirected from Set Clopen iff Boundary is Empty)Jump to navigation Jump to search
Let $T$ be a topological space, and let $H \subseteq T$.
- $\partial H = \O$
where $\partial H$ is the boundary of $H$.
From Set is Open iff Disjoint from Boundary we have that:
From Set is Closed iff it Contains its Boundary we have that: