Preprint No. A-03-02

Gerhard Preuss

A hyperspace completion for semiuniform convergence spaces and related hyperspace structures

Abstract: Since hyperspaces of complete (separated) uniform spaces are not complete in general, it is highly remarkable that in the more general context of semiuniform convergence spaces even a hyperspace completion exists which preserves several invariants, e.g. precompactness (and thus compactness), connectedness (and uniform connectedness), the property of being a filter space (or a semiuniform space), etc. This completion is used to characterize the subspaces of the compact spaces in the realm of semiuniform convergence spaces axiomatically. The complete hyperspace structure is coarser than the usual uniform hyperspace structure in case uniform spaces are considered.

Keywords: Hyperspaces, semiuniform convergence spaces, filter spaces, semiuniform spaces, Hausdorff metric, precompactness and compactness, one-point completions and generalizations

Mathematics Subject Classification (MSC2000): 54A05, 54B20, 54D30, 54E15, 54E52

Language: ENG


Contact: Gerhard Preuss, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (

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