{"title":"The interval topology on T/sub 1/-lattices","authors":"Xu Xiaoquan, Liu Yingming","doi":"10.1109/AFSS.1996.583679","DOIUrl":null,"url":null,"abstract":"The main purpose of the paper is to study under which conditions the interval topology on a T/sub 1/-lattice may be Hausdorff. The authors show that for a T/sub 1/-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 T/sub 1/-space (X, /spl part/(X)), the interval topology on /spl part/(X) cannot be Hausdorff except in the extreme case that (X. /spl part/(X)) is discrete.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"76 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/AFSS.1996.583679","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The main purpose of the paper is to study under which conditions the interval topology on a T/sub 1/-lattice may be Hausdorff. The authors show that for a T/sub 1/-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 T/sub 1/-space (X, /spl part/(X)), the interval topology on /spl part/(X) cannot be Hausdorff except in the extreme case that (X. /spl part/(X)) is discrete.
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