An example of discontinuous function on $\mathbb{R}$
100436
Examples of nowhere continuous functions
15820
Discontinuous linear functional
133231
Discontinuity of Thomae Function on $\mathbb{Q}$
22392
How can a function with a hole (removable discontinuity) equal a function with no hole?
20688
Discontinuous functions with closed graphs
112189
Discontinuity in function; order of integration matters
12639
Example of primitive function which isn't Riemann-integrable on a closed interval [0,1]
132730
Is there an everywhere discontinuous increasing function?
69724
Is Zorn's lemma necessary to show discontinuous $f\colon {\mathbb R} \to {\mathbb R}$ satisfying $f(x+y) = f(x) + f(y)$?
135610
How to give an example of a $f$ differentiable in a deleted neighborhood of $x_0$ such that $\lim_{x\to x_0}f^\prime(x)$ doesn't exist?
140445
Sequence of continuous functions whose pointwise limit is discontinuous
118400
Is there a monotonic function discontinuous over some dense set?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
154572
Continuity of a function at an isolated point
35671
Why can a discontinuous function not be differentiable?
130586
$f$ is discontinuous $\iff$ kernel($f$) is dense in X
6186
An Integrable function which is not essentially bounded on any subinterval of $[0,1]$