Does there exist a non decreasing function $f:\mathbb{R} \to \mathbb{R}$ such that the set of discontinuities is $\mathbb{Q}$?
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
151575
Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
25010
Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
24449
How discontinuous can a derivative be?
127921
Does there exist a function such that $\lim_{x \to a} f(x) = L$ for all $a \in \mathbb R$ but $f(x)$ is never $L$?
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
28191
How to show that a set of discontinuous points of an increasing function is at most countable
88240
Two functions discontinuous, but sum continuous
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
36983
Does there exist a continuous function such that f(x) is rational for every irrational x, and f(x) is irrational for every rational x?
234
No continuous function switches $\mathbb{Q}$ and the irrationals
67866
If $f:\mathbb{R}\to\mathbb{R}$ is a left continuous function can the set of discontinuous points of $f$ have positive Lebesgue measure?
24306
Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
4679
Nonpiecewise Function Defined at a Point but Not Continuous There
41043
example of discontinuous function having direction derivative