Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion
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 completi...
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Format: | Article |
Language: | English |
Published: |
Universitat Politècnica de València
2023-04-01
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Series: | Applied General Topology |
Subjects: | |
Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/18783 |
Summary: | 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. |
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ISSN: | 1576-9402 1989-4147 |