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.
Publisher
Universitat Politecnica de Valencia
Reference26 articles.
1. J. J. Adámek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1989.
2. R. Bĕlohlávek, Fuzzy Relation Systems, Foundation and Principles, Kluwer Academic/Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2002.
3. M. M. Clementino and D. Hofmann, Lawvere completeness in topology, Appl. Categ. Struct. 17 (2009), 175-210. https://doi.org/10.1007/s10485-008-9152-5
4. D. Doitchinov, Completeness in quasi-metric spaces, Topology Appl. 30 (1988), 127-148. https://doi.org/10.1016/0166-8641(88)90012-0
5. R. C. Flagg, Quantales and continuity spaces, Algebra Univers. 37 (1997), 257-276. https://doi.org/10.1007/s000120050018
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献