Prove that f is continuous for $c \in[a,b]$
62048
Proving a Lipschitz function is continuous
98772
Continuity of a function in $\mathbb{R}$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
143174
property of continuous function
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
28730
product of two uniformly continuous functions is uniformly continuous
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
61640
Prove c exists for f:[0,1] -> R
152784
$f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.
44574
Continuity of absolute value of a function
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
100740
proof of that a continuous function has a fixed point
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
40915
Proof if $f$ continuous in $x_0$ then there is a neighbourhood of $x_0$ so f bounded.