连续定向完备序半群及其范畴性质

doi:10.6040/j.issn.1671-9352.0.2015.270

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (6): 57-64.doi: 10.6040/j.issn.1671-9352.0.2015.270

连续定向完备序半群及其范畴性质

刘妮,张苗苗

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2015-06-08 出版日期:2016-06-20 发布日期:2016-06-15
作者简介:刘妮(1976— ),女,博士,副教授,研究方向为格上拓扑学与Domain理论. E-mail:niliu@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11301316);陕西省自然科学基础研究计划面上项目(2015JM1020)

Continuous directed-complete ordered semigroups and their categorical properties

LIU Ni, ZHANG Miao-miao

College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China

Received:2015-06-08 Online:2016-06-20 Published:2016-06-15

摘要/Abstract

摘要： 引入了连续定向完备序半群的概念, 得到了连续定向完备序半群的若干等价刻画, 证明了范畴CDOSG(以全体连续定向完备序半群为对象, 以保定向并的序半群同态为态射)是有限完备的, 其满子范畴CCDOSG(以全体交换的连续定向完备序半群为对象)也是有限完备的且对函数空间封闭。

关键词: D-半群同态, 序半群, 连续定向完备序半群, 有限完备范畴

Abstract: Firstly, the concept of continuous directed-complete ordered semigroup is introduced. Secondly, some equivalent characterizations of continuous directed-complete ordered semigroup are obtained. Finally, it is proved that the category CDOSG with objects all continuous directed-complete ordered semigroups and morphisms all ordered semigroup homomorphisms preserving directed sups between them is finite complete. Moreover, its full subcategory CCDOSG with objects all commutative continuous directed-complete ordered semigroups is finite complete and closed for function space.

Key words: ordered semigroup, continuous directed-complete ordered semigroup, D-semigroup homomorphism, finite complete category

中图分类号:

O153

刘妮,张苗苗. 连续定向完备序半群及其范畴性质[J]. 山东大学学报（理学版）, 2016, 51(6): 57-64.

LIU Ni, ZHANG Miao-miao. Continuous directed-complete ordered semigroups and their categorical properties[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 57-64.

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连续定向完备序半群及其范畴性质

Continuous directed-complete ordered semigroups and their categorical properties

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