可数一致连续偏序集的序同态与扩张  

Order-homomorphism and Extension of Countable Uniform Continuous Posets

作　　者：刘东明 姜广浩[1] 李辉 LIU Dongming;JIANG Guanghao;LI Hui(School of Mathematical Science, Huaibei Normal University, Huaibei 235000, Anhui)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《四川师范大学学报（自然科学版）》2019年第1期47-51,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11361028);安徽省高等学校自然科学重点项目(KJ2017A378)

摘　　要：在可数一致连续偏序集上引入序同态的概念,给出若干的等价刻画,并证明可数一致连续偏序集在保可数一致并投射下的像自身仍为可数一致连续偏序集;此外,引入可数一致基与可数一致稠密集的概念,探讨一些性质,证明它们的序同态可以唯一扩张为整个可数一致连续偏序集的序同态.In this paper,we mainly introduce order-homomorphism of countable uniform continuous posets and display some equivalent characterizations.We obtain the image of projection of preserving countable uniform sups is itself a countable uniform continuous poset.Besides,we introduce countable uniform bases and countable uniform dense sets,and study some fundamental properties of them.We show that their order-homomorphism can be uniquely extended to order-homomorphism of the entire countable uniform continuous poset.

关 键 词：可数一致连续偏序集 序同态 可数一致基 可数一致稠密集 

分 类 号：O153.1[理学—数学]