If $f\in \mathcal{C}^1(\mathbb{R}^2)$, then there exists $g:[0,1]\to \mathbb{R}^2$ such that $f\circ g $ is constant.
63836
Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
84189
Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
47026
if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$
96050
$f$ an analytic function on $\mathbb{C}$ which takes values in $\mathbb{C}\backslash(-\infty,0]$ implies constant
32789
Show bounded harmonic function on $\mathbb{C}$ is constant.
91786
Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
28399
Showing $f$ is constant
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const
61640
Prove c exists for f:[0,1] -> R
105700
Proving $\,f$ is constant.
27251
Holomorphic function with $f\circ f=f$
153411
If $|f|$ is constant, so is $f$ for $f$ analytic on a domain $D$.
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
41617
If a $C^1$ map $f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is expanding ($\|f(x)-f(y)\|\geq\|x-y\|$), which of these must be true?