Function continuous at irrationals and discontinuous at rationals
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
151427
f, g continuous for all rationals follow by continuous on all reals?
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$
46642
Continuity of $\sin(x)/x$
103241
A function that is continuous at the origin but not differentiable there
53627
Proving continuity of $f$
44574
Continuity of absolute value of a function
34940
Continuity of $f(x) = x^n$
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
41841
Function with limits only at irrational points
150833
Discontinuities of the derivative of a differentiable function on closed interval
126842
Fixed point in a continuous function
57180
Techniques to prove a function is uniformly continuous
11167
A counterexample of a differentiable function on an interval whose derivative is discontinuous
87239
Prove functions defined by sup and inf are continuous
152563
Set of discontinuity of monotone function is countable