Does this condition imply continuity?
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
15690
Is a function defined at a single point continuous?
58816
Existence of a continuous function which does not achieve a maximum.
47199
Can $\le$ be used insted of < in the definition of continuity?
84092
If $id:(X,d_1)\to (X,d_2)$ is continuous then what will be $X$?
8321
Why differentiability implies continuity, but continuity does not imply differentiability?
156996
Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$?
108734
$T$ is continuous if and only if $\ker T$ is closed
121957
Is $p\mapsto \|f\|_p$ continuous?
90152
Continuous with compact support implies uniform continuity
131062
Sequential Continuity does not imply Continuity
134752
Proof (epsilon delta) for the continuity of a function at a point
125754
Proving or disproving a statement about continuity and limits
50725
Inverse of function is continuous or not?
86327
If the absolute value of a function is continuous, is the function continuous?
62817
Functions which are Continuous, but not Bicontinuous
81223
Real Analysis Question: continuity of $f(x) = \sum_{q_n<x} 1/n^2$