Prove that the product of $n$ bounded and uniformly continuous functions are also uniformly continous
1369
two functions are uniformly continuous on some interval I and each is bounded on I then their product is also uniformly continuous on I .
158567
A uniform continuous function which is not Hölder continuous
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
60282
Prove that $f_n$ converges uniformly on $\mathbb{R}$
87239
Prove functions defined by sup and inf are continuous
68143
The set of convergent points of a sequence of continuous functions is Borel
113122
Prove that a continuous real function with finite limits is bounded
106256
Continuous mapping on a compact metric space is uniformly continuous
55749
Compactly supported continuous function is uniformly continuous
13257
How to prove this problem about uniform continuity
14067
If f uniformly continous then $|f(x)|\leq C\cdot (1+|x|)$ for constant C
99117
Existence of a sequence of positive continuous functions on $\mathbb R$ which is unbounded precisely on $\mathbb Q$
60070
Unique uniformly continuous function into complete space
58664
Proving a function is continuous for a fixed variable
36149
A uniformly continuous function maps bounded set to bounded sets