Prefilter spaces and a precompletion of preuniform convergence spaces related to some well-known completions |
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Authors: | Gerhard Preuß |
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Institution: | Institut für Mathematik, Freie Universität Berlin, Arnimallee 3, D-14195 Berlin, Germany |
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Abstract: | In non-symmetric Convenient Topology the notion of pre-Cauchy filter is introduced and the construction of a precompletion of a preuniform convergence space is given from which Wyler's completion of a separated uniform limit space O. Wyler, Ein Komplettierungsfunktor für uniforme Limesräume, Math. Nachr. 46 (1970) 1-12] as well as Weil's Hausdorff completion of a separated uniform space A. Weil, Sur les Espaces à Structures Uniformes et sur la Topologie Générale, Hermann, Paris, 1937] can be derived (up to isomorphism). By the way, the construct PFil of prefilter spaces, i.e. of those preuniform convergence space which are ‘generated’ by their pre-Cauchy filters, is a strong topological universe filling in a gap in the theory of preuniform convergence spaces. |
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Keywords: | 54A05 54A20 54E15 18A40 18D15 |
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