具有限强表示的半序集的序收敛

The Order Convergences in a Partially Ordered Set of a Finite Strong Representation

在一个半序集中可以定义网的各种序收敛,本文讨论一个半序集P及其分割完备化?中序收敛的关系、P及其强收缩中序收敛的关系,以及直积中的序收敛.主要证明了下列结果:若半序集P有一个有限强表示{P_1|i=1,…,k},那么P中的网是序收敛的当且仅当它在每一个强收缩P_i上是序收敛的.

There are a variety of known ways in which a partially ordered set P may be given a convergence.This paper discusses the relationship between order convergences of a partially ordered set P and its completion P,and its strong retraction.It is proved that a net is order convergent coordinately in a direct product of partially ordered sets.Finally,the main resut is proved:if a partially ordered set P has a finite strong representation {?},then a net X in P is order convergent if and only if X is order convergent on each P_i.