If a function is uniformly continuous on $(-\infty,-1]$ and $[-1,\infty)$ is it uniformly continuous on $\mathbb{R}$
89568
Uniform continuity on $[a,b]$ and $ [b,c]$ $\implies$ uniform continuity on $[a,c]$.
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
94244
$\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
158344
Uniform continuous maps that converge uniformly to a function f. What can we say about f?
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
60700
Continuity of a function to the integers
52632
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
90152
Continuous with compact support implies uniform continuity
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
113086
Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
40297
Proof of uniform limit of Continuous Functions
143618
If a function $f$ is continuous $\implies$ $|f|$ is continuous.(Answered by Myself)
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
152105
When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?