**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
**Available:** Pr-A-03-02.ps

**Contact**: Gerhard Preuss, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (preuss@math.fu-berlin.de)

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