given a continuous function from $f:\mathbb{Q}\to \mathbb{Q}$
24914
Does every continuous map from $\mathbb{Q}$ to $\mathbb{Q}$ extends continuously as a map from $\mathbb{R}$ to $\mathbb{R}$?
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
12349
a construction of a continuous function from a normal space to [0,1]
20199
Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
32571
Is the maximum function of a continuous function continuous?
2142
Finding a set of continuous functions with a certain property 2
130019
Function that is continuous only on the transcendental numbers
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
21269
Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
145368
How to show $f:Y\to X^{+}$ is continuous?
151410
Inequality of continuous functions
136011
Must $f$ be 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