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

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.