Abstract: To investigate the relationships among various types of continuous posets defined by the cut operator,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 established:L is s^*₂-superalgebraic,L is s₁-continuous and s₂-superalgebraic,and L is L-algebraic and s₁-continuous.

Key words: partial order set, cut operator, continuous poset, algebraic continuous poset