function $f : \mathbb{R} \to \mathbb{R}$ that $\mathbb{lim}_{x \to c} f(x) $ exists only when $c$ is irrational
41841
Function with limits only at irrational points
43189
Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
158309
Find a function that is continuous only on rationals
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
103241
A function that is continuous at the origin but not differentiable there
143798
Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
98772
Continuity of a function in $\mathbb{R}$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
145017
Example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
147184
$f:[-1,1]\to \mathbb{R}$ is a continuous function such that $f(2x^2-1)=(x^3+x)f(x).$ Find $\lim_{x\to 0}\frac {f(\cos x)}{\sin x}$