Prefilter spaces and a precompletion of preuniform convergence spaces related to some well-known completions (Q2390504)

Preuniform convergence spaces in which every pre-Cauchy filter preconverges are called precomplete. It is proved that the question of whether every preuniform convergence space has a precompletion has a positive answer. From this precompletion the Wyler completion of a separated uniform limit space as well as Weil's Hausdorff completion of a separated uniform space can be derived (up to isomorphism) by means of bireflective modifications. Moreover the construct of prefilter spaces, i.e. of those preuniform convergence spaces which are `generated' by their pre-Cauchy filters, is shown to fill a gap in the theory of preuniform convergence spaces.