Ultrafilters on ω and atoms in the lattice of uniformities I

AbstractThis is the first part of a paper devoted to atoms in the lattice of uniformities (on a given set). It is shown that there are two types of atoms: proximally discrete and proximally non-discrete. Both are related to ultrafilters. Proximally non-discrete atoms are completely described; they correspond to ultrafilters in a one-to-one way. This correspondence is used to classify ultrafilters on a countable set according as the corresponding atoms are, or are not, proximally fine