摘要
本文在偏序集上引入Scott S-集、S-基、弱逼近元等概念,得到S-超连续偏序集的几个新的刻画。证明了偏序集是S-超连续的当且仅当任不同两点可由主滤子与Scott S-集分离当且仅当它有S-基。证明了有界完备偏序集(简记为bc-poset)L是S-超连续的当且仅当任不同两点可由Scott S-余滤子集分离当且仅当完全双小于关系■具有插值性质,且L中不同点决定的完全双小于下集也不同。
In terms of the concepts of Scott S-sets, S-bases and weak approximating elements on posets, several characterizations of supercontinuity of posets are given. Main results are： A poset is supercontinuous iff every two different points can be separated by a principal filter and a Scott S-set iff it has an S-basis; A bounded complete poset （bc-poset, for short） L is supercontinuous iff every two different points can be separated by a filter which is the complement of a Scott S-set iff the completely way-below relation satisfies the interpolation property and different points in L determine different completely way-below lower sets.
出处
《模糊系统与数学》
北大核心
2017年第5期147-151,共5页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(11671008
11101212
61472343)
江苏省高校自然科学基金资助项目(15KJD110006)
江苏高校品牌专业建设工程项目(PPZY2015B109)
