Fixed points and products: Width 3
type: Item
instance of: scholarly article
title: Fixed points and products: Width 3
zbMATH Open document ID: 1037.06003
DOI: 10.1023/A:1022883828701
published in: Order
publication date: 2003-06-09T00:00:00Z
review text: We say that an ordered set \(P\) has the fixed point property (FPP), if for each endomorphism \(f\) of \(P\) there exists \(p\in P\) with \(f(p)= p\). This paper is a contribution to the general problem: ``If ordered sets \(P\) and \(X\) have FPP, does \(P\times X\) have FPP?'' In Order 11, No. 1, 11--14 (1994; Zbl 0814.06003), \textit{M. S. Roddy} solved this problem affirmatively provided that \(P\) is finite. \textit{B. Li} and \textit{E. C. Milner} [Order 12, No. 2, 159--171 (1995; Zbl 0835.06001)] and \textit{M. S. Roddy}, \textit{A. Rutkowski} and \textit{B. S. Schröder} [unpublished manuscript (1994)] (independently) extended this result to the case when \(P\) is chain complete with no infinite anti-chain. In the present paper the author solves the problem positively for \(P\) having width at most three.
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 1924893
zbMATH Keywords: finite width
zbMATH Keywords: fixed point property
zbMATH Keywords: product
zbMATH Keywords: retract
author: Micheale Susan Roddy
reviewed by: Ladislav Skula
MaRDI profile type: Publication
full work available at URL: a:1022883828701
OpenAlex ID: W1760369892
description: scientific article; zbMATH DE number 1924893