If $M$ is a subspace of a Hilbert space, then $(M^\bot)^\bot$ is the closure of $M$.
103923
Double orthogonal complement is equal to topological closure
43584
Separability and normal closure
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
95513
Proving $W$ is a subspace of $P_{2}$
50946
Separable Hilbert space have a countable orthonormal basis
19424
Showing $(M^\perp)^\perp=\overline{M}$
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
124786
Prove that V contains a subspace of each dimension
99341
Basic question: closure of irreducible sets
142014
study of subspace generated by $f_k(x)=f(x+k)$ with f continuous, bounded..
95321
Subspaces of all real-valued continuous functions on $\mathbb{R}^1$
144383
The closure of a connected set in a topological space is connected
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
152325
Every subspace of the dual of a finite-dimensional vector space is an annihilator
129549
Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
73353
Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?
125623
Subspaces of separable normed spaces