Let $D$ be a non-empty subset of Hilbert space $H$. Find $(D^\bot)^\bot$.
There was nothing about $D$ whether it is a subspace, finite or infinite dimensional.
I know that for some of these cases double orthogonal complement is equal or is a subspace of closure of $D$, but I want to systematize my knowledge.
How do I answer such question?
Would be grateful for any hints.