AFPP vs FPP
type: Item
instance of: scholarly article
title: AFPP vs FPP
zbMATH Open document ID: 1023.54033
DOI: 10.1023/A:1023017025800
author: Michael B. Smyth
author: Rueiher Tsaur
published in: Applied Categorical Structures
publication date: 2003-06-09T00:00:00Z
review text: The authors make an interesting investigation of the approximation of continuous structures (topological spaces) by discrete structures (graphs) examining the relation between fixed point properties for the two types of structures. The main theme of the paper is that almost fixed point properties of discrete structures and fixed point properties of topological spaces are interdeductible via a suitable category which contains both graphs and topological spaces as objects. Specific applications developed are: a ``digital convexity'' version of Kakutani's fixed point theorem and fixed point properties of dendrites in terms of those of finite discrete trees.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 32F17
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1925063
zbMATH Keywords: almost fixed point property
zbMATH Keywords: dendrites
zbMATH Keywords: inverse limits
zbMATH Keywords: Kakutani theorem
zbMATH Keywords: power structures
zbMATH Keywords: topological graphs
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1925063