F格上的度量问题–第二类度量
Metric Problems on F-Lattices–The Second Metric
DOI: 10.12677/AAM.2020.910215, PDF, 下载: 797  浏览: 929 
作者: 江婉文：罗格斯大学, 新伯郎士威克文理学院统计系, 美国；陈 鹏：中国科学院微电子研究所，北京
关键词: 第一类度量；第二类度量；L-实直线；R-nbd映射簇；O2-nbd映射簇；Q-CI；The First Metric； The Second Metric； L–Real Line； R-nbd Mappings； O2-nbdMappings； Q-CI
摘要: 本文研究了点式一类度量-第二类度量, 通过O2 − nbd映射簇对它进行了刻画，并进一步证明了它的诱导拓扑和它的余拓扑是一致的。另外，我们还证明了第二类度量是Q − CI的，最后，证明了L−实直线R(L)满足第二类度量和它的几个球映射的关系。
Abstract: In this paper, firstly, we investigate a kind of pointwise metric-the second metric, and characterize it by using O2 − nbd mappings. Secondly, we prove that its induced topology is consistent with its cotopology. In addition, we also prove that the second metric is Q − CI. Finally, we assert that L–real line is the second metric, and present the relationships between its several basic spheres.
文章引用：江婉文, 陈鹏. F格上的度量问题–第二类度量[J]. 应用数学进展, 2020, 9(10): 1865-1878. https://doi.org/10.12677/AAM.2020.910215

参考文献

[1] Chen, P. (2017) Metrics in L-Fuzzy Topology. China Science Press (Postdoctoral Library), Beijing. (In Chinese)
[2] Chen, P. and Shi, F.-G. (2007) Further Simplification of Erceg’s Metric and Its Properties. Advances in Mathematics, 36, 586-592. (In Chinese)
[3] Shi, F.G. (2001) Pointwise Pseudo-Metrics in L-Fuzzy Set Theory. Fuzzy Sets and Systems, 121, 200-216.
https://doi.org/10.1016/S0165-0114(00)00013-0
[4] 梁基华. 关于不分明度量空间的几个问题[J]. 数学年刊, 1984, 6A(1): 59-67.
[5] Wang, G.J. (1988) Theory of L-fuzzy Topological Space. Shanxi Normal University Publishers, Xi’an. (In Chinese)
[6] Hutton, B. (1977) Uniformities on Fuzzy Topological Spaces. Journal of Mathematical Analysis and Applications, 58, 559-571.
https://doi.org/10.1016/0022-247X(77)90192-5
[7] Shi, F.G. (2005) Pointwise Pseudo-Metric on the L-Real Line. Iranian Journal of Fuzzy Sys- tems, 4, 79-88.
[8] Shi, F.G. and Zheng, C.Y. (2005) Metrization Theorems in L-Topological Spaces. Fuzzy Sets and Systems, 149, 455-471.
https://doi.org/10.1016/j.fss.2004.02.003
[9] Peng, Y.W. (1993) Simplification of Erceg’s Fuzzy Metric Function and Its Application. Fuzzy Sets and Systems, 54, 181-189.
https://doi.org/10.1016/0165-0114(93)90275-M
[10] Engelking, R. (1977) General Topology. Polish Science Publishers, Warszawa.

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