Set convergences. An attempt of classification

Sonntag, Yves; Zălinescu, Constantin

doi:10.1090/S0002-9947-1993-1173857-8

Set convergences. An attempt of classification
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Trans. Amer. Math. Soc. 340 (1993), 199-226 Request permission

Abstract:

We endow families of nonempty closed subsets of a metric space with uniformities defined by semimetrics. Such structure is completely determined by a class (which is a family of closed sets) and a type (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.

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