Assume that f is continuous on $[0,\infty)$ and $\lim_{x\to \infty} f(x)=0$ then f is uniformly continuous
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.
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
158344
Uniform continuous maps that converge uniformly to a function f. What can we say about f?
36149
A uniformly continuous function maps bounded set to bounded sets
83494
Uniform continuity of $\ln(x)$
3856
Uniform Continuity of $x \sin x$
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
13257
How to prove this problem about uniform continuity
59519
What about the continuity of these functions in the uniform topology?
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
101701
Prove that $\ln x$ is not uniformly continuous on $(0,1]$
57642
Uniform Continuity implies Continuity
158567
A uniform continuous function which is not Hölder continuous
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.