Function continuous on every rational points but discontinuous on irrational points
102780
No function that is continuous at all rational points and discontinuous at irrational points.
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
87131
Discontinuous at rationals and differentiable at irrationals?
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
20688
Discontinuous functions with closed graphs
234
No continuous function switches $\mathbb{Q}$ and the irrationals
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?
28191
How to show that a set of discontinuous points of an increasing function is at most countable
151427
f, g continuous for all rationals follow by continuous on all reals?
88240
Two functions discontinuous, but sum continuous
103241
A function that is continuous at the origin but not differentiable there
130019
Function that is continuous only on the transcendental numbers
76396
Nowhere monotonic continuous function
60700
Continuity of a function to the integers
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
15914
Prove that any polynomial function is continuous