ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 54, 18, 60 Nusser, Harald, Free University of Berlin, Germany Completions of proabilistic semiuniform convergence spaces A probabilistic semiuniform convergence space is a pair (X, J̄), where X is a set and J̄ is a set {J^{λ} | λ ∈ [0, 1]} of semiuniform convergence structures on X satisfying two additional axioms which allow a probabilitstic interpretation:

(i) J^{λ} ⊆ J^{ν}. (ii) J^{0} is the set of all (proper) filters on X × X. The category of probasbilistic semiuniform convergence spaces and uniformly continuous maps forms a strong topological universe, which contains the category of semiuniform convergence spaces as a bireflective and bicoreflective subcategory. Completions of probabilistic semiuniform convergence spaces and certain subclasses, such as probabilistic filter spaces, probabilistic Cauchy spaces and probabilistic uniform limit spaces (= probabilistic uniform convergence spaces), will be presented. Reference: G. Preuß, Semiuniform convergence spaces, Math. Japonica 41 (1995), 465 - 491.