Preprint No. A-04-05

Gerhard Preuss

Non-symmetric convenient topology and its relations to convenient topology

Abstract: Preuniform convergence spaces are introduced as a generalization of semiuniform convergence spaces with the advantage that the construct {\bf PUConv} of preuniform convergence spaces is not only a strong topological universe, i.e., it fulfills nice convenient properties, such as the construct {\bf SUConv} of semiuniform convergence spaces, but it allows one to study even non-symmetric topological concepts as well as quasiuniform concepts. Furthermore, a completion for preuniform convergence spaces is investigated from which the usual Hausdorff completion of a separated uniform space as well as the $T_0$-quasiuniform bicompletion of a $T_0$-quasiuniform space in the sense of P. Fletcher and W. F. Lindgren can be derived.

Keywords: Preuniform convergence spaces, preconvergence spaces, quasiuniform spaces, bireflective and bicoreflective subconstructs, natural function spaces, simple completion, Hausdorff completion, bicompletion

Mathematics Subject Classification (MSC2000): 54A05, 54A20, 54C35, 54E15, 18A40

Language: ENG

Available: Pr-A-04-05.ps, Pr-A-04-05.ps.gz

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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