If $ f_n\to f $ pointwise, and $f_n $ are increasing continuous functions, and $ f $ is continuous, then $f_n\to f $ uniformly
102076
Sequence of monotone functions converging to a continuous limit, is the convergence uniform?
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
129073
If $f'$ is bounded, then $f$ is uniformly continuous
44647
Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set?
35547
Does $\{f_ng_n\}\to fg$ uniformly?
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
51247
$f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
57180
Techniques to prove a function is uniformly continuous
117502
Proving that a certain continuous function is surjective.
34940
Continuity of $f(x) = x^n$
100786
Does a continuous function take Cauchy sequences to Cauchy sequences?
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
123972
Proving that every function defined on a discrete metric space is uniformly continuous.
15284
$f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
40297
Proof of uniform limit of Continuous Functions
90152
Continuous with compact support implies uniform continuity