由Cut算子定义的多种连续偏序集之间的关系OA
Relationship Between Continuous Posets Defined by the Cut Operator
研究了由cut算子定义的多种连续偏序集之间的关系.利用Frink理想的构造证明了偏序集L为s*2-超连续偏序集当且仅当L为F-连续的s1-连续偏序集,进而给出了偏序集L为s*2-超代数偏序集、L为s1-连续的s2-超代数偏序集、L为F-代数的s1-连续偏序集等3种等价条件.
To investigate the relationships among various types of continuous posets defined by the cut op-erator,this paper uses the construction of Frink ideals to prove that a poset L is s*2-supercontinuous if and only if it is F-continuous and s1-continuous.Furthermore,the equivalence of three descriptions is es-tablished:L is s*2-superalgebraic,L is s1-continuous and s2-superalgebraic,and L is L-algebraic and s1-continuous.
梁静
淮南师范学院金融与数学学院,安徽 淮南 232001
数理科学
偏序集cut算子连续偏序集代数偏序集
partial order setcut operatorcontinuous posetalgebraic continuous poset
《吉首大学学报（自然科学版）》 2026 (4)
1-4,10,5
安徽省质量工程项目(2023JCJX021)
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