Does any example of a function continuous at rationals and discontinuous at irrationals exist?
102780
No function that is continuous at all rational points and discontinuous at irrational points.
115878
Continuous unbounded but integrable functions
89814
Limit of a Piecewise Function defined on Rationals and Irrationals
133231
Discontinuity of Thomae Function on $\mathbb{Q}$
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
130019
Function that is continuous only on the transcendental numbers
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
24817
Prove continuity on a function at every irrational point and discontinuity at every rational point.
98772
Continuity of a function in $\mathbb{R}$
120947
continuous real-valued function
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
24306
Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
131992
A problem on continuous functions
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 $x \neq 0$
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
60700
Continuity of a function to the integers
132478
Prove that continuous functions mapping irrationals to rationals must be constant