Formal balls in fuzzy quasi-metric spaces
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Authors
You Gao
- College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China.
Qingguo Li
- College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China.
Lankun Guo
- College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410012, China.
Jialiang Xie
- College of Science, Jimei University, Xiamen, 361021, China.
Abstract
The notions of Yoneda completeness and Smyth completeness on fuzzy quasi-metric spaces are introduced and their
relationship with other types of completeness including sequentially Yoneda completeness and bicompleteness are investigated.
Then we use the standard Yoneda completeness to characterize the order-theoretical properties of the poset \((BX,\sqsubseteq_M )\) of formal
balls in a fuzzy quasi-metric space \((X,M,\wedge)\). The results show that if \((BX,\sqsubseteq_M )\) is a dcpo, then \((X,M,\wedge)\) is standard complete
and conversely, \((BX,\sqsubseteq_M )\) forms a dcpo provided that \((X,M,\wedge)\) is standard Yoneda complete. Particularly, in a fuzzy metric
space, we clarify three types of completeness which can be characterized by the directed completeness of the related poset of
formal balls.
Share and Cite
ISRP Style
You Gao, Qingguo Li, Lankun Guo, Jialiang Xie, Formal balls in fuzzy quasi-metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 684--698
AMA Style
Gao You, Li Qingguo, Guo Lankun, Xie Jialiang, Formal balls in fuzzy quasi-metric spaces. J. Nonlinear Sci. Appl. (2017); 10(2):684--698
Chicago/Turabian Style
Gao, You, Li, Qingguo, Guo, Lankun, Xie, Jialiang. "Formal balls in fuzzy quasi-metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 684--698
Keywords
- Fuzzy quasi-metric space
- Yoneda complete
- standard Yoneda complete
- Smyth complete
- formal ball.
MSC
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