Super-relational fixed point property and products in ordered sets
type: Item
instance of: scholarly article
title: Super-relational fixed point property and products in ordered sets
zbMATH Open document ID: 1149.06002
published in: Order
publication date: 2008-06-03T00:00:00Z
review text: Let \(P\) be an ordered set and \(E(P)\) be the set of all endomorphisms (isotone mappings) of \(P\) into \(P\). If \(f\in E(P)\), denote by \(\text{Fix}(f)\) the set of all fixed points of \(f\), i.e., \(\text{Fix}(f):=\{p\in P:f(p)=p\}\). An ordered set \(P\) has the fixed-point property if \(\text{Fix}(f)\not=\emptyset\) for every \(f\in E(P)\). In the paper, several stronger variants of the fixed-point property are summarized and the connections among them are described. Furthermore, a new kind of such a stronger property for ordered sets, called the super-relational fixed-point property, is introduced and it is compared with strengthened and product fixed-point properties.
reviewed by: Jiří Rachůnek
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 5281945
zbMATH Keywords: fixed-point property
zbMATH Keywords: ordered set
zbMATH Keywords: product
author: Josef Niederle
MaRDI profile type: Publication
full work available at URL: s11083-007-9072-2
OpenAlex ID: W2074311928
Wikidata QID: Q37007883
cites work: Fixed points of products and the strong fixed point property
cites work: From finite posets to chain complete posets having no infinite antichain
cites work: Strengthened fixed point property and products in ordered sets
cites work: On the strong fixed point property
cites work: Fixed points and products
cites work: Fixed points and products: Width 3
cites work: Isotone relations revisited
cites work: Multifunctions and the fixed point property for products of ordered sets
cites work: THE FIXED POINT PROPERTY FOR SUMS OF POSETS
DOI: 10.1007/S11083-007-9072-2
description: scientific article; zbMATH DE number 5281945