Cauchyness and convergence in fuzzy metric spaces

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• 作者：Valentín Gregori ; Juan-José Miñana…
• 关键词：Fuzzy metric ; Cauchy sequence ; Completeness ; Compactness
• 刊名：Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：1
• 页码：25-37
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Milan
• ISSN：1579-1505
• 卷排序：111

文摘

In this paper we survey some concepts of convergence and Cauchyness appeared separately in the context of fuzzy metric spaces in the sense of George and Veeramani. For each convergence (Cauchyness) concept we find a compatible Cauchyness (convergence) concept. We also study the relationship among them and the relationship with compactness and completeness (defined in a natural sense for each one of the Cauchy concepts). In particular, we prove that compactness implies p-completeness.