Sergii Favorov: A new description of uniformly spread discrete sets

We prove that each discrete set in the Euclidean space that has bounded changes  under every translation is a bounded perturbation of a square lattice, i.e., a uniformly spread set in the sense of Laczkovich.
 

In particular, the support of every Fourier quasicrystal in the Euclidean space with unit masses is uniformly spread.