A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE
Any complex valued S-metric space where each Cauchy sequence converges to a point in this space is said to be complete. However, there are complex valued S-metric spaces that are incomplete but can be completed. A completion of a complex valued S-metric space ( is defined as a complete complex valu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitas Pattimura
2024-10-01
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| Series: | Barekeng |
| Subjects: | |
| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13851 |
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| Summary: | Any complex valued S-metric space where each Cauchy sequence converges to a point in this space is said to be complete. However, there are complex valued S-metric spaces that are incomplete but can be completed. A completion of a complex valued S-metric space ( is defined as a complete complex valued S-metric space with an isometry such that is dense in In this paper, we prove the existence of a completion for a complex valued S-metric space. The completion is constructed using the quotient space of Cauchy sequence equivalence classes within a complex valued S-metric space. This construction ensures that the new space preserves the essential properties of the original S-metric space while being completeness. Furthermore, isometry and denseness are redefined regarding a complex valued S-metric space, generalizing those established in a complex valued metric space. In addition, an example is also presented to illustrate the concept, demonstrating how to find a unique completion of a complex valued S-metric space. |
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| ISSN: | 1978-7227 2615-3017 |