If a function $f$ is continuous in $[a,∞)$ and finite $\lim_{x→+∞}⁡f(x)$ exists, then it's uniformly continuous in $[a,+∞)$.
9614
How does the existence of a limit imply that a function is uniformly continuous
33304
Let $f$ be a continuous function satisfying $\lim \limits_{n \to \infty}f(x+n) = \infty$ for all $x$. Does $f$ satisfy $f(x) \to \infty$?
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
30965
$f$ is continuous on $X$ iff $f$ is continuous on every compact subset
100979
Uniform continuity of a function and cauchy sequences
4062
prove that $f(x)=\log(1+x^2)$ is Uniform continuous with $\epsilon ,\delta$ ...
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
131060
Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
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?
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
129716
Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
152784
$f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.
157821
Let $S$ be a finite set. Show that any function $f: S \rightarrow \mathbb{R}^n$ is continuous on S. What if $S$ is countably infinite?
138105
Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?