If $f$ is continuous and bounded on $\Bbb{R}$, does it mean that $f$ is uniformly continuous on $\Bbb{R}$?
132946
Continuous and bounded imply uniform continuity?
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
101906
Why is this sequence of equicontinuous functions uniformly bounded?
15284
$f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
24017
Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?
124779
Intuition for uniform continuity of a function on $\mathbb{R}$
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
44647
Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set?
155822
Does uniform convergence preserves absolute continuity?
51247
$f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
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
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
102918
Prove $\sin x$ is uniformly continuous on $\mathbb R$
12408
Prove that a function whose derivative is bounded is uniformly continuous.
2118
Are continuous functions with compact support bounded?
136011
Must $f$ be continuous?