**Preprint No.**
A-98-10

#
Gerhard Preuß

## Characterizations of Subspaces of important types of convergence spaces in the realm of Convenient Topology

**Abstract:** Since in Convenient Topology
we are mainly concerned with semiuniform convergence spaces, the question
arises how the subspaces of important types of convergence spaces
such as topological spaces, pretopological spaces (=closure spaces
in the sense of \v{C}ech [5]), limit spaces ( in the sense of
Kowalsky [10] and Fischer [6]) or Kent convergence spaces can be
characterized when they are considered as semiuniform convergence
spaces (provided all convergence spaces fulfill a certain symmetry
condition). This paper presents the solution. Furthermore, the
relationships to other important subconstructs of the construct {\bf
SUConv} of semiuniform convergence spaces are investigated.
**Keywords: **Semiuniform convergence spaces, filter spaces, sublimit spaces, subpretopological spaces, subtopological spaces, bireflective (resp.\ bicoreflective) subconstructs

**Mathematics Subject Classification (MSC91):** 54A05 Topological spaces and generalizations (closure spaces, etc.)
, 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

**Language:** ENG
**Available:** Pr-A-98-10.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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