Prove continuous function from R to Z is constant
727
Prove that any continuous integer-valued function of a real variable is constant.
39921
show that f is constant on I
89050
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
47474
Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
158519
Hints for a complex limit: Prove if $\lim_{z \to \infty} f(z)/z = 0$ then $f(z)$ is constant.
53726
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
29276
technique of proving continuity complex function
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
82367
Prove that a holomorphic function with postive real part is constant
87239
Prove functions defined by sup and inf are continuous
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
150447
Prove a differentiable function between banach spaces is continuous
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
104044
Prove continuous functions $f$ and $g$ are equal
28399
Showing $f$ is constant