Set convergences. An attempt of classification

Abstract

We endow families of nonempty closed subsets of a metric space with uniformities defined by semimetrics. Such structure is completely determined by a <italic>class</italic> (which is a family of closed sets) and a <italic>type</italic> (which is a semimetric). Two types are sufficient to define (and classify) almost all convergences known till now. These two types offer the possibility of defining other set convergences.