Statistical convergence in functional spaces

One of the main questions in analysis is what precisely must be added to pointwise convergence of a sequence of continuous functions to preserve continuity of the limit function? In 1883 Arzela gave a necessary and sufficient condition via quasi-uniform convergence for the pointwise limit of a sequence of real-valued continuous functions on a compact interval to be continuous. Arzela's work initiated a study that led to several outstanding papers. Caserta, A. and et al. offer a direct proof of the equivalence of Arzela and Alexandroff conditions using statistical convergence. In this study, we examine the statistical versions of several classical kinds of convergence of sequences of functions introduced by Caserta (Caserta, 2011) from a topological space to a metric space.