For $A \subset \Bbb{R}^n$, show $A^{\circ} =\left(\overline{(A^c)}\right)^c$
44912
Prove that $ \overline {A^\complement} = (A°)^\complement $
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
65297
Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$.
19424
Showing $(M^\perp)^\perp=\overline{M}$
69673
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
63465
Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
121886
Proving image of $f:D^n\rightarrow \mathbb{R}^n \;$ contains $\;D^n$
47056
Show that the boundary of a set equals the boundary of its complement
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
70959
Prove that a set $E$ is closed iff it's complement $E^{c}$ is open
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
31710
Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
137711
Alternative proof that $[\Bbb{Q}(\zeta_n) : \Bbb{Q} ]= \varphi(n)$ uses circular reasoning?