Monopolonium is a monopole-antimonopole bound state, whose lifetime grows as the cube of the initial diameter. Such objects are important because their decay products can be observable. Apart from the monopolonium, it is believed that the existence of an epoch when the U(1) of the electromagnetism is spontaneously broken ensures the efficient annihilation of monopoles and antimonopoles in the U...

The well-known “splitting necklace theorem” of Alon [1] says that each necklace with k · ai beads of color i = 1, . . . , n can be fairly divided between k “thieves” by at most n(k − 1) cuts. Alon deduced this result from the fact that such a division is possible also in the case of a continuous necklace [0, 1] where beads of given color are interpreted as measurable sets Ai ⊂ [0, 1] (or more g...