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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… Click to show full abstract
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.
Keywords:
non symmetric;
theory completeness;
cauchy;
quasi cauchy;
cauchy spaces
Journal Title: Applied General Topology
Year Published: 2023
Link to full text (if available)
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Journal Title: Applied General Topology
Year Published: 2023
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!