existence of a function that is continuous at every rational and discontinuous at every irrational
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
83204
Is every $G_\delta$ set the set of continuity points of some function $f$?
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
102780
No function that is continuous at all rational points and discontinuous at irrational points.
60070
Unique uniformly continuous function into complete space
11167
A counterexample of a differentiable function on an interval whose derivative is discontinuous
34940
Continuity of $f(x) = x^n$
15487
Continuous function from a connected set?
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
57180
Techniques to prove a function is uniformly continuous
132478
Prove that continuous functions mapping irrationals to rationals must be constant
134752
Proof (epsilon delta) for the continuity of a function at a point
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
102075
A function continuous on all irrational points
73594
Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$