Convergence methods on suprametric spaces

This thesis aims to extend the standard idea of convergence to examine many generalized forms of convergence inside of suprametric spaces. The concepts of statistical convergence, rough statistical convergence and lacunary-statistical convergence are presented, along with their applications in suprametric spaces. The thesis analyzes the main features of the different convergence types, their interactions, and their comparison with classical convergence. Additionally, example sequences are provided for each method, the benefits of suprametric are highlighted, and several theorems are established to support the theoretical foundation of these methods. The results show that suprametric structures provide greater mathematical flexibility compared to standard metric structures.