Completeness in quasi-uniform spaces

Author: Andrikopoulos, Athanasios

Source: Acta Mathematica Hungarica, Volume 105, Numbers 1-2, October 2004 , pp. 151-173(23)

Publisher: Springer

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Abstract:

We introduce a theory of completeness (the π-completeness) for quasi-uniform spaces which extends the theories of bicompleteness and half-completeness and prove that every quasi-uniform space has a π-completion. This theory is based on a new notion of a Cauchy pair of nets which makes use of couples of nets. We call them cuts of nets and our inspiration is due to the construction of the τ-cut on a quasi-uniform space (cf. [1], [20]). This new version of completeness coincides with bicompletion, half-completion and D-completion in extended subclasses of the class of quasi-uniform spaces.

Keywords: bicompletion; quasi-uniform space; D-completion; net-conet

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:AMHU.0000045540.39991.f2

Publication date: 2004-10-01