Proving if f has a continuous extension to [a,b] then f is uniformly continuous on (a,b).
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
55749
Compactly supported continuous function is uniformly continuous
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
102457
for any $A\subseteq X$, $f(\overline{A})\subseteq\overline{f(A)}$ , if and only if $f: X \to Y$ is continuous.
124779
Intuition for uniform continuity of a function on $\mathbb{R}$
125682
Proof verification: the product of two continuous functions is continuous
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
62270
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
113871
Prove $f(x) = \sqrt x$ is uniformly continuous on $[0,\infty)$
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
150554
proof that $f'$ is continuous at $a$
90152
Continuous with compact support implies uniform continuity
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous