چكيده به لاتين
The present research investigates and analyzes bipolar metric spaces and their applications in
various fields, including homotopy, Lebesgue integration, and user behavior in online shopping
and social networks. The bipolar metric space, as a mathematical structure, provides a
framework for examining distances and relationships between elements of two distinct sets.
These characteristics are particularly significant in analyzing behavioral patterns of users on social
media platforms such as Instagram and Twitter.
This study begins with an introduction to metric spaces and the specific features of bipolar metric
spaces. It then explores homomorphic mappings and their impact on preserving topological
structures within metric spaces.
In the applied section of this research, the behavior of Iranian and foreign users on Instagram is
examined. Utilizing bipolar metric spaces, the purchasing patterns and interactions of users are
analyzed. The results of this analysis indicate that cultural and social differences between Iranian
and foreign users have a significant impact on their shopping behaviors and usage of social
networks.
Finally, this research demonstrates how these tools can be used to design more targeted
marketing strategies for attracting and retaining users. The findings from this study can assist
businesses in optimizing their services and providing a better user experience by gaining a deeper
understanding of user behavior.
