Topos中偏序对象的上(下)确界

doi:10.6040/j.issn.1671-9352.0.2015.430

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (4): 112-117.doi: 10.6040/j.issn.1671-9352.0.2015.430

Topos中偏序对象的上(下)确界

卢涛¹,王习娟^2*,贺伟³

1.淮北师范大学数学科学学院, 安徽淮北 235000;2.南京大学数学系, 江苏南京 210097;3.南京师范大学数学科学学院, 江苏南京 210097

收稿日期:2015-10-15 出版日期:2016-04-20 发布日期:2016-04-08
通讯作者: 王习娟(1969— ), 女, 博士, 副教授, 研究方向为domain理论, 范畴论. E-mail:wangxijuan69@163.com E-mail:lutao7@live.com
作者简介:卢涛(1974— ), 男, 博士, 副教授, 研究方向为topos理论, 范畴论, locle理论. E-mail:lutao7@live.com
基金资助:
国家自然科学基金资助项目(11571175);安徽省高校自然科学研究重点项目(KJ2015A064)

The supremum and infimum of partially ordered objects in a topos

LU Tao¹, WANG Xi-juan^2*, HE Wei³

1. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China;
2. Department of Mathematics, Nanjing University, Nanjing 210097, Jiangsu, China;
3. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, Jiangsu, China

Received:2015-10-15 Online:2016-04-20 Published:2016-04-08

摘要/Abstract

摘要： 基于topos中的偏序对象, 讨论了topos中的上下确界的定义, 推广了格论中的经典结论, 将一些格论中熟知的结论提升到了topos中。得到了主要结果:topos中的对象为完备偏序对象当且仅当该对象的任意广义子集存在上(下)确界。

关键词: 偏序对象, 完备偏序对象, topos, 上(下)确界

Abstract: The concepts of supremum and infimum which are common generalizations of lattice theory is introduced, and some well-known lattice theory into an arbitrary topos is lifted. The main result that an object in a topos is a complete partially ordered object if and only if its general subset has supremum and infimum is obtianed.

Key words: partially ordered object, supremum(infimum), topos, complete partially ordered object

中图分类号:

O189.11

卢涛,王习娟,贺伟. Topos中偏序对象的上(下)确界[J]. 山东大学学报（理学版）, 2016, 51(4): 112-117.

LU Tao, WANG Xi-juan, HE Wei. The supremum and infimum of partially ordered objects in a topos[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 112-117.

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Topos中偏序对象的上(下)确界

The supremum and infimum of partially ordered objects in a topos

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