Some other properties of convex sets are valid as well.

For general closed convex sets, the limit point need not be the projection.

Cubes can be deformed so long as they remain convex set.

The Hilbert metric of a convex set is defined in a similar way.

An interval in a partially ordered vector space is a convex set.

There are more than one hyperplane separating a closed convex set and a point lying outside of it.

A note concerning extremal points of a convex set.

The conical hull of a set S is a convex set.

The space of all functions on the real line is a convex set, and has the homotopy type of one point.

It is clear from the definition that the family of separable states is a convex set.

The restriction of the Lebesgue measure to any convex set is also log-concave.

A convex set is connected; it is actually simply connected.

Any convex set can be described as the (possibly infinite) intersection of half-spaces.

This can be used to describe certain geometric properties of convex sets analytically.

A credal set is often assumed or constructed to be a closed convex set.

Convex sets are often studied with probability theory.

Any non-empty convex set is a star domain.

Moreover there exists a neighbourhood basis for 0 consisting of absorbing and convex sets.

There is an elegant proof using Minkowski's theorem about convex sets.

In mathematics, a convex curve is the boundary of a convex set.

In fact, to every convex set, the Minkowski gauge associates a continuous linear functional.

Convex analysis, the study of convex sets and functions.

The uniform distribution over any convex set.

For any nonempty convex set then is a convex cone.

(For the collection of all convex sets, connect the dots!)