Fixed simplex property for retractable complexes
type: Item
instance of: scholarly article
title: Fixed simplex property for retractable complexes
zbMATH Open document ID: 1213.54065
DOI: 10.1155/2010/303640
author: Adam Idzik
author: Anna Zapart
published in: Fixed Point Theory and Applications
publication date: 2010-12-13T00:00:00Z
full work available at URL: https://eudml.org/doc/231042
review text: The following are the main results of the paper: I) A star has the fixed point property; II) If an \(\leq n\)-complex is retractable, then it has the fixed point property; III) From an \(s\)-recursively retractable complex \(K_{\leq n}\), by a sequence of retractions, one can obtain the complex generated by any simplex \(S\in K_{\leq n}\). Some applications to graph theory of the obtained results are then given.
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 57Q99
Mathematics Subject Classification ID: 54C15
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 5825808
zbMATH Keywords: Simplex
zbMATH Keywords: star
zbMATH Keywords: fixed point
zbMATH Keywords: recursively contractible complex
zbMATH Keywords: dunce cap
zbMATH Keywords: graph
zbMATH Keywords: tree
zbMATH Keywords: loop
zbMATH Keywords: fixed clique property.
MaRDI profile type: Publication
Wikidata QID: Q59253085
OpenAlex ID: W2060841708
cites work: The Kakutani property and the fixed point property of topological spaces with abstract convexity
cites work: Fixed-edge theorem for graphs with loops
cites work: A fixed-point theorem for trees
description: scientific article; zbMATH DE number 5825808