区间值模糊拟度量空间的一些拓扑性质  

On some topological properties of interval-valued fuzzy quasi-metric spaces

作　　者：陆汉川[1] 李生刚[2] 

机构地区：[1]贵州大学理学院,贵州贵阳550025 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《云南大学学报（自然科学版）》2016年第2期171-177,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11271297);中央高校基本科研业务费专项资金(14SZYB08);贵州大学引进人才科研基金(201504)

摘　　要：在拟度量的背景下推广了区间值模糊度量的概念,得到了通过拟度量诱导的拓扑与通过标准的区间值模糊拟度量诱导的拓扑是相一致的.证明了每一个拟可度量化的拓扑空间允许有一个相兼容的区间值模糊拟度量.相反,通过区间值模糊拟度量生成的拓扑是拟可度量化的.此外,讨论了双完备化的区间值模糊拟度量空间的一些性质.证明了一个区间值模糊拟度量空间如果有双完备化,则它是唯一达到等距同构的.We generalize the notions of interval-valued fuzzy metric in the quasi-metric background,obtained that topology through the quasi-metric induced and through the standard interval-valued fuzzy quasi-metric induced is consistent.It is proved that every quasi-metrizable topological space admits a compatible interval-valued fuzzy quasi-metric. On the contrary,the topology generated by interval-valued fuzzy quasi-metric is quasi-metrizable.In addition,some properties of the bicomplete interval-valued fuzzy quasi-metric is discussed.It is proved that if there is an interval- valued fuzzy quasi-metric space which has bicompletion,then it is unique up to isometry.

关 键 词：区间值模糊拟度量空间 拟度量 拟一致结构 双完备化 等距同构 

分 类 号：O189.13[理学—数学]