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Meet-continuity on $L$-directed Complete Posets | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 5، دوره 10، شماره 5، دی 2013، صفحه 63-78 اصل مقاله (358.4 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2013.1207 | ||
| نویسندگان | ||
| Shuhua Su1؛ Qingguo Li* 2؛ Lankun Guo2 | ||
| 1College 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 | ||
| 2College of Mathematics and Econometrics, Hunan University, Chang- sha 410082, P.R. China | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| $L$-dcpo؛ Generalized Scott topology؛ Meet-continuity | ||
| مراجع | ||
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