Analogizing Hutton's quasi-uniformities for complete lattices and extending Shi's quasi-uniformities to closed set lattices

作者：Yao Wei^*; Lu Ling Xia

来源：Fuzzy Sets and Systems, 2009, 160(9): 1233-1244.

DOI：10.1016/j.fss.2008.07.011

• Topology
• Closed set lattice
• Co-topology
• Co-nucleus
• Hutton quasi-uniformity
• Shi pointwise quasi-uniformity

This paper gives analogies of Hutton's quasi-uniformities for complete lattices and extensions of Shi's pointwise quasi-uniformi ties to closed set lattices. CL(GOH) denotes the category of all complete lattices with generalized order homomorphisms as motphisms and CSL the category of all closed set lattices. HQUnif and SPQUnif denote the categories of Hutton quasi-uniform spaces on complete lattices and Shi pointwise quasi-uniform spaces on closed set lattices, respectively. We prove that both HQUnif and SPQUnif are fibre-complete topological categories over CLGOH and CSL with respect to the expected forgetful functors, respectively. Also, a mistake in W. Kotze [Uniform spaces, in: U. Hohle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, Vol. 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999, pp. 553-580] is pointed out.

• 出版日期2009-5-1
• 单位河北科技大学; 河北地质大学