A new type of statistical Cauchy sequence and its relation to Bourbaki completeness. Issue 1 (1st January 2018)

• Record Type: Journal Article
• Authors: Ilkhan, Merve; Kara, Emrah Evren
• Editors: Srivastava, Hari M.
• Is Part Of: Cogent mathematics & statistics. Volume 5:Issue 1(2018)
• Publication Date: 2018-01-01
• Subjects: Bourbaki–Cauchy sequences -- Bourbaki completeness -- Bourbaki boundedness -- statistical convergence -- asymptotic density; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematics; Statistics; Periodicals; 510
• DOI: 10.1080/25742558.2018.1487500
• Languages: English
• ISSNs: 2574-2558

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.