Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion

• Jäger, Gunther ^[1]
  1. [1] University of Applied Sciences

     University of Applied Sciences

     Region Hannover, Alemania

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 1, 2023, págs. 205-227
• Idioma: inglés
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• Resumen

  • Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces.