If $f$ is continuous on $[0, \infty)$ and uniformly continuous on $[b, \infty)$ for some $b > 0$ then $f$ is unif. continuous on $[0, \infty).
126212
Proving uniform continuity on an interval
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
36166
Uniform continuity on (0,1) implies boundedness
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
129073
If $f'$ is bounded, then $f$ is uniformly continuous
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
100979
Uniform continuity of a function and cauchy sequences
143174
property of continuous function
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
84785
Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
55749
Compactly supported continuous function is uniformly continuous
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
34940
Continuity of $f(x) = x^n$
53627
Proving continuity of $f$
129716
Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that