Example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points
97619
Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
126759
Unbounded continuous function on non-compact metric space
124997
finding examples for a non negative and continuous function for which the infinite integral is finite but the limit at infinity doesn't exist
110258
Continuous but not uniformly continuous example
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
2321
Can there be two distinct, continuous functions that are equal at all rationals?
127921
Does there exist a function such that $\lim_{x \to a} f(x) = L$ for all $a \in \mathbb R$ but $f(x)$ is never $L$?
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
139763
A function takes every function value twice - proof it is not continuous
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 $\mathbb R$
133696
Example of a function continuous at only one point.
144426
Example of a function $f:\mathbb{R}^2\to\mathbb{R}$ not differentiable at $(0,0)$, but has a directional derivative at $(0,0)$ in all directions
4679
Nonpiecewise Function Defined at a Point but Not Continuous There
76607
Show that exists a continuous function in $E$ that is not bounded
18082
A continuous function that attains neither its minimum nor its maximum at any open interval is monotone
140445
Sequence of continuous functions whose pointwise limit is discontinuous