Cauchyness and convergence in fuzzy metric spaces

被引：27

作者：

Gregori, Valentin ^{[1
]}

Minana, Juan-Jose ^{[1
]}

Morillas, Samuel ^{[1
]}

Sapena, Almanzor ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia, Spain

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2017年 / 111卷 / 01期

关键词：

Fuzzy metric; Cauchy sequence; Completeness; Compactness; FIXED-POINT THEOREMS; CONTRACTIVE MAPPINGS;

D O I：

10.1007/s13398-015-0272-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：25 / 37

页数：13

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