Extension of Shi's quasi-uniformities in a Kubiak–Šostak sense

作者：Yueli Yue; Jinming Fang

来源：Fuzzy Sets and Systems, 2006, 157(14): 1956-1969.

• Fuzzy co-topology
• Fuzzy quasi-uniformity
• Fuzzy remote neighborhood system

The aim of this paper is to study the extension of Shi Fu-Gui's quasi-uniformities in a Kubiak–Šostak sense. The relationship between this extension of Shi Fu-Gui's quasi-uniform molecular lattices (Shi's QUML) and the corresponding Kubiak–Šostak extension of Wang Guo-Jun's topological molecular lattices (Wang's TML) is discussed. QUML and TML denote the categories of Shi's QUML and Wang's TML, respectively. CD is the category of completely distributive lattices with complete lattice morphisms as morphisms. We prove that FQUML—the category of fuzzy quasi-uniform molecular lattices (the extension of Shi's QUML)—is a topological category over CDop and FTML—the category of fuzzy topological molecular lattices (the extension of Wang's TML)—can be embedded in FQUML. We also prove that FQUML is isomorphic to QUMLc(M) when M is a completely distributive lattice with multiplicative property, where QUMLc(M) is the co-tower extension of QUML. Finally, we study the Kubiak–Šostak extension of Hutton's quasi-uniformities.