Pseudodiscrete balleans - Protasova, O.I. (Algebra and Discrete Mathematics, 2006)
A ballean B is a set X endowed with some family
of subsets of X which are called the balls. The properties of the
balls are postulated in such a way that a ballean can be considered
as an asymptotic counterpart of a uniform topological space. A ballean is called pseudodiscrete if "almost all" balls of every pregiven
radius are singletons. We give a filter characterization of pseudodiscrete balleans and their classification up to quasi-asymorphisms. It
is proved that a ballean is pseudodiscrete if and only if every real
function defined on its support is slowly oscillating. We show that
the class of irresolvable balleans are tightly connected with the class
of pseudodiscrete balleans.