Completeness in quasi-uniform spaces (Journal article)

Andrikopoulos, A.

We introduce a theory of completeness (the -completeness) for quasi-uniform spaces which extends the theories of bicompleteness and halfcompleteness and prove that every quasi-uniform space has a -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 -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.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Οικονομικών και Κοινωνικών Επιστημών. Τμήμα Οικονομικών Επιστημών
Keywords: quasi-uniform space,D-completion,net-conet,bicompletion
Appears in Collections:Άρθρα σε επιστημονικά περιοδικά ( Ανοικτά)

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