Is $ f \colon (1, +\infty) \to \mathbb{R} , f(x) = \sin \frac{1}{x} $ uniformly continuous?
94244
$\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
135449
Prove: $\frac1x$ is not a uniformly continuous function
15579
Show that $f$ is uniformly continuous if limit exists
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
98772
Continuity of a function in $\mathbb{R}$
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
65346
Characterisation of uniformly continuous function
129073
If $f'$ is bounded, then $f$ is uniformly continuous
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
13257
How to prove this problem about uniform continuity
93461
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
77322
Uniform continuity of $\sin(x\sin x )$ for all $x\in (0,\infty)$
95429
If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
12408
Prove that a function whose derivative is bounded is uniformly continuous.
66758
$f_n:[0,1]\to [0,1]$ continuous, $f_n\to f$ uniformly, prove: ${\frac1n}\sum_{k=1}^{n}{f_k} \to f$ uniformly
158344
Uniform continuous maps that converge uniformly to a function f. What can we say about f?