关键词: Scott S-集, 交S-超连续偏序集, S-超连续偏序集, 分配格

Abstract: The concept of meet supercontinuity for posets is introduced. Properties and characterizations of meet supercontinuity, as well as relationships of meet supercontinuity with supercontinuity and quasi supercontinuity are given. Main results are: （1）[A] lattice which is also meet supercontinuous must be distributive; （2）[A] bounded complete poset（bc-poset, for short）[L] is meet supercontinuous iff [?x∈L] and every subset [A] for which [∨A] exists, one has [x∧∨A=∨x∧a:a∈A]; （3）[A] bounded complete poset is supercontinuous iff it is meet supercontinuous and quasi supercontinuous; （4）Some counterexamples are constructed to show that a distributive complete lattice needn’t be a meet supercontinuous lattice and a continuous lattice needn’t be a meet supercontinuous lattice.

Key words: Scott S-set, meet supercontinuous poset, supercontinuous poset, distributive lattice