Abstract:We study several kinds of statistical convergence of sequences of functions with values in semi-uniform spaces. Particularly, we generalize to statistical convergence the classical results of C.~Arzel\`a, Dini and P.\,S.~Alexandroff, as well as their statistical versions studied in [Caserta A., Di Maio G., Ko\v{c}inac L.\,D.\,R., {\it Statistical convergence in function spaces},. Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.] and [Caserta A., Ko\v{c}inac L.\,D.\,R., {\it On statistical exhaustiveness}, Appl. Math. Lett. {\bf 25} (2012), no.~10, 1447--1451].
Keywords: statistical convergence; semi-uniform space; sequence; function; continuity
DOI: DOI 10.14712/1213-7243.2015.231
AMS Subject Classification: 54E15 54A20 40A30 40A35