S₂-quasialgebraic Posets

Based on the Dedeking-MacNeille completion operator,we introduce the con-cept of s2-quasialgebraic posets.Some properties of S2-quasialgebraic posets are investigated.The main results are as follow:(1)A poset is S2-algebraic if and only if it is both S2-quasialgebraic and meet S2-continuous;(2)A poset is S2-quasialgebraic poset if and only if its weak Scott topology is hypercontinuous and algebraic lattice.