$f = \{(x,e^x) \mid x \in \mathbb Z\}$ Is $f$ continuous on its domain?
73585
Why is the function continuous, if it is defined only on integers?
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
131060
Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
17310
Can $f(x)=|x|^3$ be differentiated
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
135863
Is the graph of a continuous function homeomorphic to its domain?
59519
What about the continuity of these functions in the uniform topology?
62947
If $f(x)$ is equal to $x$ or $1-x$ when $x$ is rational/irrational, then $f$ is continuous only at $x=1/2$
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
150554
proof that $f'$ is continuous at $a$
118048
Can a function with just one point in its domain be continuous?
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
145368
How to show $f:Y\to X^{+}$ is continuous?
113975
Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function