Prove that there exists a monotone nondecreasing function $f:[0,1] \rightarrow \mathbb{R}$ discontinuous in rationals
101230
Example of an increasing, integrable function $f:[0,1]\to\mathbb{R}$ which is discontinuous at all rationals?
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
130586
$f$ is discontinuous $\iff$ kernel($f$) is dense in X
140445
Sequence of continuous functions whose pointwise limit is discontinuous
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
54137
Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable
58816
Existence of a continuous function which does not achieve a maximum.
35264
Must a monotone function have a monotone derivative?
76396
Nowhere monotonic continuous function
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
107772
Separability of functions with compact support
133231
Discontinuity of Thomae Function on $\mathbb{Q}$
118400
Is there a monotonic function discontinuous over some dense set?
147546
$f: \mathbf{R} \rightarrow \mathbf{R}$ monotone increasing $\Rightarrow$ $f$ is measurable
43001
Proof for Dirichlet Function and discontinuous
22210
Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$