Prefilter spaces and a precompletion of preuniform convergence spaces related to some well-known completions

摘要

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 fuer uniforme Limesraeume, Math. Nachr. 46 (1970) 1-12] as well as Weil's Hausdorff completion of a separated uniform space [A. Weil, Sur les Espaces a Structures Uniformes et sur la Topologie Generate, 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.