论文标题
同时有序关系的Galois连接和同构
Galois connections and isomorphism of simultaneous ordered relations
论文作者
论文摘要
在理论顺序的情况下，部分有序的集合仅配备一个关系，该关系决定了集合的整个结构/HASSE图。在本文中，我们介绍了如何在我们称为二进制posets的同时部分有序的关系下研究部分有序的集合。本文是由在两个不同的部分有序关系下同时操作集合的问题的动机。已经表明，二进制poset遵循二元性原理，就像posets一样。在此框架内，还提出了一些有关最大和最小元素的新定义。此外，得出了一些关于同构和GALOIS连接的定理。
In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper, we have presented how partially ordered sets can be studied under simultaneous partially ordered relations which we have called binary posets. The paper is motivated by the problem of operating a set simultaneously under two distinct partially ordered relations. It has been shown that binary posets follow the duality principle just like posets do. Within this framework, some new definitions concerning maximal and minimal elements are also presented. Furthermore, some theorems on order isomorphism and Galois connections are derived.
