If $f$ is continuous on $\left[ a,b\right]$ then $f$ is uniformly continuous on $\left[ a,b\right]$.
90152
Continuous with compact support implies uniform continuity
55368
$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly
30965
$f$ is continuous on $X$ iff $f$ is continuous on every compact subset
67866
If $f:\mathbb{R}\to\mathbb{R}$ is a left continuous function can the set of discontinuous points of $f$ have positive Lebesgue measure?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
138397
If a sequence of functions $f_n$ converges uniformly to $f$, does this imply $f_n$ is continuous? How to prove?
149827
show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
129073
If $f'$ is bounded, then $f$ is uniformly continuous
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
40915
Proof if $f$ continuous in $x_0$ then there is a neighbourhood of $x_0$ so f bounded.
40297
Proof of uniform limit of Continuous Functions
53627
Proving continuity of $f$
44269
If $f$ is nonnegative and continuous on $[a,b]$, then $\left(\int_a^b f(x)^n \ dx\right)^{1/n}\to\max\limits_{[a,b]} f$
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const
46101
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$