Prove that a convex function on $\mathbb{R}^n$ is continuous
60521
Continuity of a convex function
67313
Proving $\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$ is convex
116382
Showing convexity of a function with the restriction over an arbitrary line
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
13257
How to prove this problem about uniform continuity
17223
Continuity of an inverse function.
86305
A secant inequality for convex functions
132869
Show that any bounded linear functional on a normed linear space is continuous
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
15924
Convexity and strong lower semicontinuity imply weak lower semicontinuity
158399
Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
143174
property of continuous function
57180
Techniques to prove a function is uniformly continuous
143936
Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?