Order Extensions and the Fixed Point Property |
| |
Authors: | Imed Zaguia |
| |
Institution: | (1) Department of Mathematics & Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khoud 123, Muscat, Sultanate of Oman |
| |
Abstract: | 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.
Part of this work was done while the author was visiting Brandon University. The author thanks M. Roddy for his hospitality
and financial support. |
| |
Keywords: | Ordered set Fixed point Dismantlability Irreducible element Retractable element Order preserving map Minimal automorphic |
本文献已被 SpringerLink 等数据库收录! |
|