S-超连续偏序集的性质及等价刻画

计算机工程与应用 ›› 2015, Vol. 51 ›› Issue (1): 9-12.

S-超连续偏序集的性质及等价刻画

毛徐新1，徐罗山2

1.南京航空航天大学理学院，南京 210016
2.扬州大学数学科学学院，江苏扬州 225002

出版日期:2015-01-01 发布日期:2015-01-06

Properties and characterizations of supercontinuous posets

MAO Xuxin1, XU Luoshan2

1.College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2.College of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu 225002, China

Online:2015-01-01 Published:2015-01-06

摘要/Abstract

摘要： 研究偏序集上的S-超连续性以及与其他广义连续性间的若干关系。利用提升和主理想S-超连续等概念给出了S-超连续性的几个等价刻画。证明了一个交半格是S-超连续的当且仅当它是主理想S-超连续的。构造了反例说明偏序集的S-超连续性与主理想S-超连续性互不蕴涵。

关键词: S-超连续偏序集, 主理想S-超连续, 交半格, Scott拓扑

Abstract: Some properties of supercontinuity of posets and relations with other generalized continuities are given. The concept of principal ideal supercontinuity for posets is introduced. By lifts and principal ideals, some new characterizations for supercontinuous posets are given. It is proved that the supercontinuity is equivalent to the principal ideal supercontinuity on semilattices. Two counterexamples are constructed to show that the supercontinuity and the principal ideal supercontinuity on posets do not imply each other.

Key words: supercontinuous poset, principal ideal supercontinuous, semilattice, Scott topology

毛徐新1，徐罗山2. S-超连续偏序集的性质及等价刻画[J]. 计算机工程与应用, 2015, 51(1): 9-12.

MAO Xuxin1, XU Luoshan2. Properties and characterizations of supercontinuous posets[J]. Computer Engineering and Applications, 2015, 51(1): 9-12.

[1]	毛徐新1，徐罗山2. 交S-超连续偏序集[J]. 计算机工程与应用, 2017, 53(4): 15-18.
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