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Convergence and completeness in fuzzy metric spaces and fuzzifying uniform spaces
YUE Yue-Li
School of Mathematical Sciences, Ocean University of China, Qingdao 266100
*Correspondence author
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Funding: National Natural Science Foundation of China (No. 11201437); the specialized Research Fund for the Doctoral Program of Higher Education（No.No.20110132120014）
Opened online:30 November 2015
Accepted by: none
Citation: YUE Yue-Li.Convergence and completeness in fuzzy metric spaces and fuzzifying uniform spaces[OL]. [30 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4665152
 
 
The aim of this paper is to study convergence and completeness in fuzzy metric spaces and fuzzifying uniform spaces from a degree point of view. Firstly, the convergence degree theory of sequence in fuzzy metric spaces are given. Secondly, the relationship between compactness, total boundedness and completeness is studied. Thirdly, the corresponding filter convergence theory and completeness degree theory in fuzzifying uniform spaces are investigated. Finally, the relationship between the completeness of fuzzy metric spaces and that of induced fuzzifying uniform spaces is studied.
Keywords:fuzzy mathematics; fuzzy metric; fuzzifying uniformity; convergence; compactness; completeness
 
 
 

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