Inclusion of orthogonal complements: if $U_1\subset\ U_2$, then $U_2^\bot\subset\ U_1^\bot$
132487
Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$
113326
Proving orthogonality of vectors in a complex vector space
12459
Associativity of symmetric difference of sets
119003
Complement of $c_{0}$ in $\ell^{\infty}$
92802
Proof of Borsuk-Ulam Theorem .
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
54377
Complementability of von Neumann algebras
48579
How to find the orthogonal complement of a subspace?
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
73338
Prove that the closure of complement, is the complement of the interior
88595
Prob. 21, Sec. 17 in Munkres' TOPOLOGY, 2nd ed: Closure and complementation can result in at most 14 different sets
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
47056
Show that the boundary of a set equals the boundary of its complement
79826
$gHg^{-1}\subset H$ whenever $Ha\not = Hb$ implies $aH\not =bH$
95928
Independence and orthogonality
146455
Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$