Absolutely convex set

An absolutely convex set is like a big bowl of jelly beans, where the jelly beans are arranged in a way that you can draw a straight line between any two jelly beans inside the bowl and all the jelly beans along that line are also inside the bowl. This means that the bowl is not only curved on the outside, but also on the inside.

In math terms, an absolutely convex set is a collection of points where if you take any two points inside the set, you can draw a straight line between them and all the other points on that line are also inside the set. This is different from a regular convex set, which only requires that the line between two points lies completely inside the set, but not necessarily all the points on that line.

Basically, an absolutely convex set is like a bowl that extends both on the outside and on the inside, while a regular convex set is like a bowl that only extends on the outside.