If $f$ is symmetrically continuous, then $f$ is not necessarily continuous
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
58816
Existence of a continuous function which does not achieve a maximum.
145368
How to show $f:Y\to X^{+}$ is continuous?
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
145017
Example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points
22641
Nonlinear function continuous but not bounded
144001
If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
7876
If $f(x+y)=f(x)+f(y) ,\forall\;x,y\in\Bbb{R}$, then if $f$ is continuous at $0$, then it is continuous on $\Bbb{R}.$
150554
proof that $f'$ is continuous at $a$
131992
A problem on continuous functions
88240
Two functions discontinuous, but sum continuous
86327
If the absolute value of a function is continuous, is the function continuous?
30036
Function in $H^1$, but not continuous
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
128719
Are constants the only continuous functions with "symmetric derivative" zero?
112409
If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing