Completion of Semiuniform Convergence Spaces |
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Authors: | Gerhard Preuß |
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Affiliation: | (1) Department of Mathematics, Free University of Berlin, Germany |
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Abstract: | Semiuniform convergence spaces form a common generalization of filter spaces (including symmetric convergence spaces [and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform convergence space a completion is constructed, called the simple completion. This one generalizes Császár's -completion of filter spaces. Thus, filter spaces are characterized as subspaces of convergence spaces. Furthermore, Wyler's completion of separated uniform limit spaces can be easily derived from the simple completion. |
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Keywords: | semiuniform convergence spaces filter spaces uniform convergence spaces (= uniform limit spaces) completions universal constructions |
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