MathDB

Suppose that we have a countable set

A

of balls and a unit cube in

\mathbb R^3

. Assume that for every finite subset

B

A

it is possible to put all balls of

B

into the cube in such a way that they have disjoint interiors. Show that it is possible to arrange all the balls in the cube so that all of them have pairwise disjoint interiors.

Problem Statement