Why does a closed convex set contain lines if and only it has no extreme points?
94231
Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
14448
Elementary proof that $|x|^p$ is convex.
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
138457
Seminorms: Absolute Convexity
77217
Proof that a coordinate-wise convex function is convex?
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
15645
Is convex open set in $\mathbb{R}^n$ is regular?
32110
$\forall x,y\in\partial S$, the line connecting $\{x,y\}$, $L\{x,y\}\cap\partial S=\{x,y\}$, then $S$ must be either convex or concave?
72659
How can we define convexity in one dimension?
136022
Why can't a union of two intervals be the maximum existence interval of a solution?
121095
Is convex hull of a finite set of points in $\mathbb R^2$ closed?
55995
Why is the supremum of the empty set $-\infty$ and the infimum $\infty$?
55661
Existence of two disjoint closed sets with zero infimal distance
69283
The limit points of an open interval (open set)
58101
The set of points where two maps agree is closed?
116382
Showing convexity of a function with the restriction over an arbitrary line
115376
Is $(-\infty,3]\cap(0,1)^c\cap[-1,\infty)$ closed? Open? What are interior points?