Find a function that is continuous only on rationals
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
151427
f, g continuous for all rationals follow by continuous on all reals?
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
132478
Prove that continuous functions mapping irrationals to rationals must be constant
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
120947
continuous real-valued function
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
120935
Why is every continuous function on the reals determined by its value on rationals?
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
128911
Continuous extension of a real function
76607
Show that exists a continuous function in $E$ that is not bounded
154572
Continuity of a function at an isolated point
34836
Composition of Absolutely Continuous Functions
46834
show that a distance function is continuous
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
126878
Monotonic function satisfying darboux property $\Rightarrow$ continuous
53738
Monotone functions and continuity