Differentiable function which sends rationals to rationals and irrationals to irrationals
849
$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
122519
Multiplicative Functions
120784
Differentiablility over closed intervals
143491
Show that $f$ is differentiable on $(−1, 1)$.
8039
an analytic function from unit disk to unit disk with two fixed point
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
100319
Functional equation with strange property about irrational numbers
30523
A binary irrational with bits defined by primes
41767
Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
27265
Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
57233
Proof of continuity of Thomae Function at irrationals.
67791
Can I exchange limit and differentiation for a sequence of smooth functions?
143593
A sequence of differentiable functions that converge uniformly to a non differentiable function - is my example correct?
158309
Find a function that is continuous only on rationals
156839
Functions Which are non differentiable on a Given Set.
91736
Explicit homeomorphism between open and closed rational intervals?