On the Regularity of the Kowalsky Completion

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Abstract
Cauchy spaces were introduced by Kowalsky in 1954 [9]. In that paper a first completion method for these spaces was given. In 1968 Keller [5] has shown that the Cauchy space axioms characterize the collections of Cauchy filters of uniform convergence spaces in the sense of [1]. Moreover in the completion theory of uniform convergence spaces the associated Cauchy structures play an essential role [12]. This fact explains why in the past ten years in the theory of Cauchy spaces, much attention has been given to the study of completions.

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