Author:
Author:
Athanasios Andrikopoulos
Athanasios Andrikopoulos
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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.
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| Acta Mathematica Hungarica | |
|---|---|
| Language | English |
| Size | B5 |
| Year of Foundation |
1950 |
| Volumes per Year |
3 |
| Issues per Year |
6 |
| Founder | Magyar Tudományos Akadémia  |
| Founder's Address |
H-1051 Budapest, Hungary, Széchenyi István tér 9. |
| Publisher | Akadémiai Kiadó Springer Nature Switzerland AG |
| Publisher's Address |
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11. |
| Responsible Publisher |
Chief Executive Officer, Akadémiai Kiadó |
| ISSN | 0236-5294 (Print) |
| ISSN | 1588-2632 (Online) |
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