Meet-continuity on $L$-directed Complete Posets

Document Type : Research Paper


1 College 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. China

2 College of Mathematics and Econometrics, Hunan University, Chang- sha 410082, P.R. China


In this paper, the definition of meet-continuity on $L$-directed
complete posets (for short, $L$-dcpos) is introduced. As a
generalization of meet-continuity on crisp dcpos, meet-continuity on
$L$-dcpos, based on the generalized Scott topology, is
characterized. In particular, it is shown that every continuous
$L$-dcpo is meet-continuous and $L$-continuous retracts of
meet-continuous $L$-dcpos are also meet-continuous. Then, some
topological properties of meet-continuity on $L$-dcpos are
discussed. It is shown that meet-continuity on $L$-dcpos is a
topological invariant with respect to the generalized Scott
topology, and meet-continuity on $L$-dcpos is hereditary with
respect to generalized Scott closed subsets.


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