continuity at zero implies continuity everywhere
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 $\Bbb{R}.$
98666
Continuity defined for rational and irrational numbers
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
97975
Does factor-wise continuity imply continuity?
57839
Real analysis: density and continuity
71487
Real Analysis: Continuity of a Composition Function
64619
Continuity of a function of product spaces
12107
How is the epsilon-delta definition of continuity equivalent to the following statement?
156996
Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$?
128911
Continuous extension of a real function
76965
The epsilon-delta definition of continuity
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
42084
Set of points of continuity are $G_{\delta}$
157603
Continuity $\iff$ Preimage is closed whenever set is closed
125754
Proving or disproving a statement about continuity and limits
141366
Absolutely continuity and Lipschitz-like continuity
9320
Extension of continuous function on a closed subset of $\mathbb{R}$