Continuous Function taking rationals to irrationals and vice versa
234
No continuous function switches $\mathbb{Q}$ and the irrationals
60700
Continuity of a function to the integers
43189
Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
15487
Continuous function from a connected set?
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
41767
Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
153495
Continuous function does not map closed set to closed set
12240
Problem with a continuous function
40719
Give a concrete sequence of rationals which converges to an irrational number and vice versa.
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
22408
Jutifying: irrational + rational = irrational
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
24817
Prove continuity on a function at every irrational point and discontinuity at every rational point.
102075
A function continuous on all irrational points
131992
A problem on continuous functions
89814
Limit of a Piecewise Function defined on Rationals and Irrationals