Let $z$ be a point in a metric space $(X, p)$. Why is $f: X\to\mathbb{R}$, $f(x)=p(x,z)$ uniformly continuous?
45581
Is the distance function in a metric space (uniformly) continuous?
59519
What about the continuity of these functions in the uniform topology?
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
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?
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
62723
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
113086
Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
138397
If a sequence of functions $f_n$ converges uniformly to $f$, does this imply $f_n$ is continuous? How to prove?
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
65346
Characterisation of uniformly continuous function
45395
Difference between continuity and uniform continuity
95327
Lipschitz and uniform continuity
136011
Must $f$ be continuous?
47419
Asymptotics of uniformly continuous functions over $\mathbb R$
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
155822
Does uniform convergence preserves absolute continuity?