Title :
The interval topology on T1-lattices
Author :
Xiaoquan, Xu ; Yingming, Liu
Author_Institution :
Dept. of Math., Jiangxi Normal Univ., Nanchang, China
Abstract :
The main purpose of the paper is to study under which conditions the interval topology on a T1-lattice may be Hausdorff. The authors show that for a T1-lattice L, the interval topology on L cannot be Hausdorff except in the extreme case that L is isomorphic to the power set of some set X. Similarly, for a T1-space (X, ∂(X)), the interval topology on ∂(X) cannot be Hausdorff except in the extreme case that (X. ∂(X)) is discrete
Keywords :
fuzzy set theory; lattice theory; set theory; topology; Hausdorff separation axiom; T1-lattices; interval topology; power set; set; Algebra; Lattices; Mathematics; Power generation; Topology;
Conference_Titel :
Fuzzy Systems Symposium, 1996. Soft Computing in Intelligent Systems and Information Processing., Proceedings of the 1996 Asian
Conference_Location :
Kenting
Print_ISBN :
0-7803-3687-9
DOI :
10.1109/AFSS.1996.583679
