Continuity on $\mathbb{R}$
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
95321
Subspaces of all real-valued continuous functions on $\mathbb{R}^1$
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
61375
Meaning of $\mathbb{R}[x]$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
34940
Continuity of $f(x) = x^n$
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
138815
For which conditions on countable sets does continuity implies uniform continuity
63598
Is every separately continuous function on $R^2$ continuous?
44574
Continuity of absolute value of a function
154572
Continuity of a function at an isolated point
131060
Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
136011
Must $f$ be continuous?
59519
What about the continuity of these functions in the uniform topology?
17223
Continuity of an inverse function.