Is every convex function on an open interval continuous?
31548
Proof of "every convex function is continuous"
78229
Proving that the tangent to a convex function is always below the function
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
97382
Continuous differentiability implies Lipschitz continuity
104257
$C^1$ functions on an open connected set and local Lipschitz continuity
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
40438
Proving that closed (and open) balls are convex
157731
Show that one-sided limits always exist for a monotone function (on an interval)
136011
Must $f$ be continuous?
71001
Do continuous linear functions between Banach spaces extend?
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
75882
Countability of local maxima on continuous real-valued functions
71619
Proving that a convex function is Lipschitz
9451
Show bounded and convex function on $\mathbb R$ is constant
77217
Proof that a coordinate-wise convex function is convex?