A new type of statistical Cauchy sequence and its relation to Bourbaki completeness

Abstract

Abstract Bourbaki complete metric spaces are important since they are a class between compact metric spaces and complete metric spaces. The aim of the present paper is to introduce the statistical Bourbaki–Cauchy sequence as a new concept and to give an equivalent condition for a metric space to be Bourbaki complete. Also, Bourbaki complete and Bourbaki-bounded metric spaces are characterized in terms of functions which preserve statistical Bourbaki–Cauchy sequences.