If $f$ and $g$ are bounded and uniformly continuous prove that $fg$ is uniformly continuous
69122
If $f,g$ are uniformly continuous prove $f+g$ is uniformly continuous but $fg$ and $\dfrac{f}{g}$ are not
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
3856
Uniform Continuity of $x \sin x$
69716
$f_x$ is Borel measurable and $f^y$ is continuous then $f$ is Borel measurable
158423
How to prove that if $f$ is continuous a.e., then it is measurable.
89568
Uniform continuity on $[a,b]$ and $ [b,c]$ $\implies$ uniform continuity on $[a,c]$.
10747
Given function $g$ continuous in line $[0,\infty)$...
55368
$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly
147021
Proving a function is bounded
118207
Prove that the product of two continuous functions is continuous
106256
Continuous mapping on a compact metric space is uniformly continuous
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
130023
Prove that the sum of two continuous functions is continuous
47188
Uniformly Continuous Function sending Bounded Set to Unbounded One
65346
Characterisation of uniformly continuous function
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
54499
How do I show that all continuous periodic functions are bounded and uniform continuous?