Prove that $f(\overline C ) \subset \overline{ f(C)}$ .
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
145039
Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
117502
Proving that a certain continuous function is surjective.
61640
Prove c exists for f:[0,1] -> R
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
19424
Showing $(M^\perp)^\perp=\overline{M}$
86317
Show that $F\subset Y$ is closed in $Y$ iff $F=Y\;\cap\;H$ where $H\subset X$ is closed in $X$.
123613
Double Complement of a set proof
18877
$f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic
111205
Proving that $\lim_{k\to \infty}\frac{f(x_k)-f(y_k)}{x_k-y_k}=f'(c)$ where $\lim_{k\to \infty}x_k=\lim_{k\to \infty}y_k=c$ with $x_k<c<y_k$
53528
If $\ker f\subset \ker g$ where $f,g $ are non-zero linear functionals then show that $f=cg$ for some $c\in F$.
24050
Characterization of the Closure of a Set
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
70361
if a complex function $f$ is real-differentiable, then $f$ or $\overline{f}$ are complex-differentiable