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L-连续偏序集的M性质与有限分离性
  • 时间：0
  • 分类：O159.1[理学—数学;理学—基础数学] O189.1[理学—数学;理学—基础数学]
  • 作者机构：[1]南京师范大学数学与计算机科学学院,南京210097, [2]连云港师范高等专科学校,江苏连云港222006, [3]江南大学理学院,江苏无锡214063
  • 相关基金：致谢 衷心感谢审稿人的仔细审阅及有益意见.国家自然科学基金（No.10731050）资助的项目.
  • 相关项目：不确定性处理的数学理论、方法及其应用
关键词： L-连续偏序集, M性质, FS—domain, 相容domain, Continuous L-poset, Property M, FS-domain, Consistent domain
中文摘要：

讨论了L-连续偏序集的M性质与有限分离性质之间的关系，主要结果：（1）若P为L-连续偏序集，则P是有限上集生成，而且满足M性质当且仅当它的定向完备化为FS—domain（有限分离的domain）；（2）若P为相容L—domain，则P是有限上集生成，而且满足M性质当且仅当它为相容FS—domain．

英文摘要：

This paper investigates the relation between continuous L-posets with property M and FS-domains. The main results are： （1） Let P be a continuous L-poset. Then P is finitely generated （as an upper set） and satisfies property M with respect to the basis P if and only if the directed completion of P is an FS-domain. （2） If P is a consistent L-domain, then P is finitely generated （as an upper set） and satisfies property M with respect to the basis P if and only if P is a consistent FS-domain.

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