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


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

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