University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065410520131029Meet-continuity on $L$-directed Complete Posets6378120710.22111/ijfs.2013.1207ENShuhuaSuCollege of Mathematics and Econometrics, Hunan University, Chang-
sha 410082, P.R. CHINA and College of Science, East China Institute of Technology,
Fuzhou, JiangXi 344000, P.R. ChinaQingguoLiCollege of Mathematics and Econometrics, Hunan University, Chang-
sha 410082, P.R. ChinaLankunGuoCollege of Mathematics and Econometrics, Hunan University, Chang-
sha 410082, P.R. ChinaJournal Article20110627In this paper, the definition of meet-continuity on $L$-directed<br />complete posets (for short, $L$-dcpos) is introduced. As a<br />generalization of meet-continuity on crisp dcpos, meet-continuity on<br />$L$-dcpos, based on the generalized Scott topology, is<br />characterized. In particular, it is shown that every continuous<br />$L$-dcpo is meet-continuous and $L$-continuous retracts of<br />meet-continuous $L$-dcpos are also meet-continuous. Then, some<br />topological properties of meet-continuity on $L$-dcpos are<br />discussed. It is shown that meet-continuity on $L$-dcpos is a<br />topological invariant with respect to the generalized Scott<br />topology, and meet-continuity on $L$-dcpos is hereditary with<br />respect to generalized Scott closed subsets.https://ijfs.usb.ac.ir/article_1207_9b5017f23e1aef5ba45329046156f1b4.pdf