Function $\mathbb{R}\to\mathbb{R}$ that is continuous and bounded, but not uniformly continuous
37812
Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
148931
Constructing a function that is continuous and has a max on an open interval, but is not necessarily increasing immediately to the left of the max.
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
148328
Example of a function $f$ on $X$ to $\mathbb{R}$ which is not $X$-measurable but $|f|$, and $f^2$ are measurable.
103241
A function that is continuous at the origin but not differentiable there
54499
How do I show that all continuous periodic functions are bounded and uniform continuous?
117419
Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
55749
Compactly supported continuous function is uniformly continuous
47419
Asymptotics of uniformly continuous functions over $\mathbb R$
30036
Function in $H^1$, but not continuous
1014
Pointwise limit of continuous functions not Riemann integrable
115878
Continuous unbounded but integrable functions
126759
Unbounded continuous function on non-compact metric space
158940
Give an example of a continuous function $f : [0, ∞) \mapsto [0, ∞)$ such that $\int_{0}^{\infty}f(x)dx$ exists but $f$ is unbounded.
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
123981
Is it possible to write any bounded continuous function as a uniform limit of smooth functions