Is $f:[0,1] \to \{0,1\}$ constant?
103568
Possibility of finding a such function?
97371
Proving a function is constant, under certain conditions?
99827
For what values will f(x) be necessarily one-one?
128719
Are constants the only continuous functions with "symmetric derivative" zero?
113385
Example of $f,g: [0,1]\to[0,1]$ and Riemann-integrable, but $g\circ f$ is not?
81264
Is $[0, 1) \times (0, 1)$ homeomorphic to $(0, 1) × (0, 1)$?
38257
Continuous bijection from $(0,1)$ to $[0,1]$
26388
proof that function is constant
132113
Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?
63590
Let $g$ be a function from $(0, 1)$ to $\mathbb{R}$ and $\int_0^1 g^2(x)dx$ finite. Does this imply that $\int_0^1 g(x)dx$ is finite?
61190
If all derivatives of $f$ are uniformly bounded by a common constant and $f(1/n) = 0$ for all $n$, is $f$ identically zero?
140602
If the absolute value of an analytic function $f$ is a constant, must $f$ be a constant?
130748
Infinitely differentiable function with given zero set?
73547
Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
145984
if $f: (0,\infty) \to (0,\infty)$ is a strictly decreasing then $f \circ f$ is decreasing?
118306
$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?