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

被引：8
|
作者：
Ilkhan, Merve [1 ]
Kara, Emrah Evren [1 ]
机构：
[1] Duzce Univ, Dept Math & Stat, Duzce, Turkey
来源：
COGENT MATHEMATICS & STATISTICS | 2018年 / 5卷 / 01期
关键词：
Bourbaki-Cauchy sequences; Bourbaki completeness; Bourbaki boundedness; statistical convergence; asymptotic density;
D O I：
10.1080/25742558.2018.1487500
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：9
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