Abstract The aim of this paper is to study the theory of weighted (pseudo-quasi-)metrics based on L-fuzzy sets. We first prove that the category of weighted pointwise quasi-metric spaces is isomorphic to that of L-partial metric spaces. Then we introduce the remote-neighborhood mapping and use it to characterize the L-partial pseudo-quasi-metric. Finally, we investigate properties of the L-topology induced by the L-partial pseudo-quasi-metrics.

中文翻译：

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L-部分度量及其拓扑

摘要 本文的目的是研究基于L-模糊集的加权（伪准）度量理论。我们首先证明加权逐点拟度量空间的范畴与L-部分度量空间的范畴同构。然后我们引入了远邻映射并用它来刻画 L 部分伪准度量。最后，我们研究了由 L 部分伪准度量引起的 L 拓扑的性质。