if fn converges uniformly to f then f is continuous
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
9614
How does the existence of a limit imply that a function is uniformly continuous
40297
Proof of uniform limit of Continuous Functions
34940
Continuity of $f(x) = x^n$
28730
product of two uniformly continuous functions is uniformly continuous
90152
Continuous with compact support implies uniform continuity
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
15579
Show that $f$ is uniformly continuous if limit exists
153854
$X_{n}$ converges in probability, $f$ is continuous, $f(X_{n})$ converges in probability
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
101701
Prove that $\ln x$ is not uniformly continuous on $(0,1]$
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
60282
Prove that $f_n$ converges uniformly on $\mathbb{R}$
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
55749
Compactly supported continuous function is uniformly continuous
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
126212
Proving uniform continuity on an interval