$f$ continuous on open set implies locally Lipschitz. What additional condition will make it true?
59859
Locally Lipschitz implies continuity. Does the converse implication hold?
65346
Characterisation of uniformly continuous function
100740
proof of that a continuous function has a fixed point
152976
Real Analysis: open and closed sets
29154
$f$ is continuous and open implies $f$ injective
127739
Is a continuous function on a bounded set bounded itself?
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
60521
Continuity of a convex function
55368
$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?
97382
Continuous differentiability implies Lipschitz continuity
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
30965
$f$ is continuous on $X$ iff $f$ is continuous on every compact subset
43874
Differentiability implies continuity - A question about the proof
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.
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$