Statistical convergence in topological function spaces

In this thesis, the concept of statistical convergence is examined within the framework of topological function spaces equipped with semi-uniform structures. After presenting the historical background and fundamental notions, the semi-uniform convergence topology is investigated, and new definitions of statistical convergence for semi-uniform valued sequences of functions are introduced. The equivalence between pointwise and uniform statistical convergence is studied in the obtained topological function spaces, and results concerning the continuity of limit functions in locally uniform spaces are established. In the final part, possible directions for future research are discussed, and a list of references consulted throughout the study is provided.