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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (2): 64-71.doi: 10.6040/j.issn.1671-9352.0.2015.481

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Topos中完备偏序对象上的算子理论

卢涛1,王习娟2*,贺伟3   

  1. 1.淮北师范大学数学科学学院, 淮北 安徽 235000;2.南京大学数学系, 南京 江苏 210097;3.南京师范大学数学科学学院, 南京 江苏210097
  • 收稿日期:2015-10-15 出版日期:2016-02-16 发布日期:2016-03-11
  • 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(11171156);安徽省高校自然科学研究重点项目(KJ2015A064)

The operator theory on complete partially ordered objects in a topos

LU Tao1, WANG Xi-juan2*, HE Wei3   

  1. 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 Science, Nanjing Normal University, Nanjing 210097, Jiangsu, China
  • Received:2015-10-15 Online:2016-02-16 Published:2016-03-11

摘要: 研究了完备偏序对象间的投射算子, 给出了闭包算子和核算子的等价刻画, 将一些格论中的经典结论推广到了topos中。

关键词: 核算子, 投射算子, 完备偏序对象, 闭包算子, 偏序对象

Abstract: The concept of the projective operators between complete partially ordered objects in a topos is investigated. The characterizations of the closure operator and the kernel operator in a topos are given, which are common generalizations of the classical lattice theory.

Key words: partially ordered object, projective operator, complete partially ordered object, closure operator, kernel operator

中图分类号: 

  • O189.11
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[11] 卢涛, 王习娟, 贺伟. Topos中选择公理的一个等价刻画[J]. 山东大学学报(理学版), 2015, 50(12):1-5. LU Tao, WANG Xijuan, HE Wei. An equivalent characterization of the choice axiom in a Topos[J]. Journal of Shandong University(Natural Science), 2015, 50(12):1-5.
[1] 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.
[2] 卢涛, 王习娟, 贺伟. Topos中选择公理的一个等价刻画[J]. 山东大学学报(理学版), 2015, 50(12): 54-57.
[3] 张艳霞,李生刚*,鲜路. M-闭包空间的积、和与商[J]. J4, 2010, 45(4): 74-76.
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