Order Extensions and the Fixed Point Property

Imed Zaguia

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Order Extensions and the Fixed Point Property

机译：订单扩展和定点属性

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The purpose of this paper is to investigate how the fixed point property and its negation behave when a covering relation is added to the order. We prove that every finite ordered set which is not totally ordered and which is dismantlable by retractables, respectively by irreducibles, has an upper cover (in its extension lattice) which is also dismantlable by retractables, respectively by irreducibles. We also provide examples of finite ordered sets having the fixed point property so that none of their upper covers has the fixed point property.

机译：本文的目的是研究将覆盖关系添加到定单时定点属性及其取反的行为。我们证明，每个不是完全有序的并且可由伸缩件分别由不可约简分解的有限有序集，都有一个上盖（在其延伸网格中），该上盖也可由伸缩件分别由不可约简分解。我们还提供了具有定点属性的有限有序集的示例，因此它们的上封面都不具有定点属性。

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来源
《Order》 |2008年第3期|p.267-279|共13页
作者
Imed Zaguia;
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作者单位

Department of Mathematics & Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khoud 123, Muscat, Sultanate of Oman;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
ordered set; fixed point; dismantlability; irreducible element; retractable element; order preserving map; minimal automorphic;

机译：有序集;不动点;可分解性;不可约元素;可伸缩元素;保序图;最小自同构;

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Order Extensions and the Fixed Point Property

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