On Stoltenberg's quasi-uniform completion

09/01/2020

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by   Athanasios Andrikopoulos, et al.

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In this paper, we give a new completion for quasi-uniform spaces which generalizes the completion theories of Doitchinov [8] and Stoltenberg [20]. The presented completion theory is very well-behaved and extends the completion theory of uniform spaces in a natural way. That is, the definition of Cauchy net and the constructed completion coincide with the classical in the case of uniform spaces. The main contribution this completion theory makes is the notion of the cut of nets which generalize the idea of Doitchinov for the notion of-Cauchy net [1]