If $f$ is holder continuous for $\alpha >1$ then $f$ is constant.
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
9614
How does the existence of a limit imply that a function is uniformly continuous
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
136011
Must $f$ be continuous?
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
86517
If $|f(z)|\le |g(z)|$, can we say $f$ is constant?
158423
How to prove that if $f$ is continuous a.e., then it is measurable.
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
113343
$f$ is constant if derivative equals zero
113975
Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
53627
Proving continuity of $f$
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
56127
Prove a function is constant under certain conditions
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
91352
If $\Re(f)$ is bounded then f is constant.
137043
To show that function is constant