Prove that convex set has empty interior if and only of there exists a hyperplane containing the set.
110845
Convex Set with Empty Interior Lies in an Affine Set
25738
Jensen's Inequality implies convexity?
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
87207
Prove that the support function of an arbitrary set $A\subset\mathbb R^n$ is convex
49721
Prove the empty set is closed for a metric space (X,d).
1307
Infimum and supremum of the empty set
116851
Show that f(x) is convex
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
28391
Prove the compactness of a set B
39020
Why is empty set an open set?
94231
Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
81351
Polish space in which the interior of each compact set is empty
113922
Proof that the intersection of any finite number of convex sets is a convex set
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
73338
Prove that the closure of complement, is the complement of the interior
53132
A convex subset of a set has 'smaller' boundary than the set?
58277
If nonempty, nonsingleton $Y$ is a proper convex subset of a simply ordered set $X$, then $Y$ is ray or interval?