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Completeness in fuzzy metric spaces based on $I$-filters
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.Completeness in fuzzy metric spaces based on $I$-filters[OL]. [30 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4665155
 
 
The aim of this paper is to study completeness in fuzzy metric spaces and $I$-uniform spaces based on $I$-filters. It is shown that the degree to which fuzzy metric space is complete is equal to the degree to which its induced $I$-uniform space is complete, this is to say that the fuzzy metric space is complete if and only if the induced $I$-uniform space is complete.
Keywords:fuzzy mathematics;fuzzy metric; $I$-uniformity; $I$-filter; completeness
 
 
 

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