%0 Journal Article
%T Topos中偏序对象的上(下)确界<br>The supremum and infimum of partially ordered objects in a topos
%A 卢涛
%A 王习娟
%A 贺伟&lt
%A br&gt
%A LU Tao
%A WANG Xi-juan
%A HE Wei
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2015.430
%X 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。<br>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
%K 偏序对象
%K 完备偏序对象
%K topos
%K 上(下)确界
%K &lt
%K br&gt
%K partially ordered object
%K supremum(infimum)
%K topos
%K complete partially ordered object
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.430