ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 54A05 54A20 54B30 54C35 54E05 54E15 Leseberg, Dieter, UB Braunschweig + FU Berlin Filterconvergence as a convenient concept for Topology It has been a trend in Categorical Topology to embed topological categories into better behaved topological categories, i. e. topological universes or strong topological universes. The topological universe of semiuniform convergence spaces introduced by Preuss form a common generalization of symmetric limit spaces and uniform limit spaces, moreover it is cartesian closed, hereditary and the product of quotients are again quotients. In this note we define and study the so called filterunitopic spaces which are a common generalization of semiuniform convergence spaces and the supertopologies as defined by Doitchinov. It is cartesian closed , and we also show that the generalized convergence spaces in the sense of Kent are nothing else than special filterunitopic spaces.