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s2-连续性的遗传性和映射不变性
The Hereditary and Invariant Properties of s2-continuity
【摘要】 基于正规完备化算子,本文讨论了s2-连续性和s2-拟连续性的遗传性和映射不变性。主要结果有:（1）s2-连续性,s2-交连续性与s2-拟连续性对弱Scott开集都是可遗传的;（2）s2-连续性,s2-交连续性和s2-拟连续性对弱Scott闭集一般不具有遗传性;（3）s2-连续偏序集的连续收缩与s2-连续偏序集在弱Scott连续的核映射下的像还是s2-连续的;（4）s2-拟连续偏序集的连续收缩与s2-拟连续偏序集在弱Scott连续的核映射下的像仍是s2-拟连续的。
【Abstract】 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 continuous 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.
【Key words】 s2-continuous Poset； s2-quasicontinuous Poset； Continuous Retract； Kernel Operator； Hereditary Property；
- 【文献出处】 模糊系统与数学 ,Fuzzy Systems and Mathematics , 编辑部邮箱 ,2019年06期
- 【分类号】O153.1
- 【下载频次】24