The Hereditary And Invariant Properties Of S₂-continuity

In this paper,based on the Dedekind-MacNeille completion operator,the hereditary and invariant properties of s2-continuity are discussed.The main results are:(1)s2-continuity、meet s2-continuity and s2-quasicontinuity are hereditary for weak Scott open sets;(2)s2-continuity、meet s2-continuity and s2-quasicontinuity are generally not hereditary for weak Scott close sets;(3)The continuous contraction of s2-continuous posets and the image of s2-continuity under the continuous kernel operator with respect to the weak Scott topology are still s2-continuous;(4)The con-tinuous contraction of s2-quasicontinuous posets and the image of s2-quasicontinuity under the continuous kernel operator with respect to the weak Scott topology are still s2-quasicontinuous.