L-连续偏序集的M性质与有限分离性

The Property M and Finite Separatedness of Continuous L-Posets

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.

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.