| 具有限强表示的半序集的序收敛 |
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| 引用本文： | 仝道荣.具有限强表示的半序集的序收敛[J].河海大学学报(自然科学版),1993(5). |
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| 作者姓名： | 仝道荣 |
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| 作者单位： | 河海大学数学物理系 |
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| 摘 要： | 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.
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| 关 键 词： | 半序集 序收敛 强收缩 有限强表示 |
The Order Convergences in a Partially Ordered Set of a Finite Strong Representation |
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| Tong Daorong,Dept.of Mathematics and Physics,Hohai Univ..The Order Convergences in a Partially Ordered Set of a Finite Strong Representation[J].Journal of Hohai University (Natural Sciences ),1993(5). |
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| Authors: | Tong Daorong Deptof Mathematics and Physics Hohai Univ |
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| Abstract: | 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. |
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| Keywords: | partially ordered set order convergence strong retraction finite strong representation |
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