A Completion Theorem for Complex Valued S-metric Space
Year: 2024
Type: article
Abstract: 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.
Authors: Mariatul Kiftiah, Yundari Yundari, Suryani Suryani, Nover Lauren
Institution: Tanjungpura University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403412972