Decompositions of factor maps involving bi-closing maps
type: Item
instance of: scholarly article
title: Decompositions of factor maps involving bi-closing maps
zbMATH Open document ID: 0898.58016
DOI: 10.1007/BF01332825
published in: Monatshefte für Mathematik
publication date: 1998-11-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178805
review text: Consider a factor map \(\theta\) from an irreducible shift of finite type \(\sigma\) onto a sofic shift \(S\). The main result of the paper is the existence of a decomposition into factor maps \(\theta= \gamma\circ \phi\) where \(\phi\) maps onto another shift of finite type, and \(\gamma\) is bi-closing. Recall that a factor map is bi-closing if it never identifies two points which are asymptotic by the shift, in either direction. The proof is constructive. In general, it is impossible to postulate that the degrees of \(\theta\) and \(\gamma\) should be equal. Necessary and sufficient conditions for that are given.
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 1145819
zbMATH Keywords: shift of finite type
zbMATH Keywords: sofic shift
author: Paul B. Trow
reviewed by: Grzegorz Świątek
MaRDI profile type: Publication
cites work: Q3744431
cites work: Topological entropy and equivalence of dynamical systems
cites work: A Note on Minimal Covers for Sofic Systems
cites work: Resolving maps and the dimension group for shifts of finite type
cites work: Endomorphisms of irreducible subshifts of finite type
cites work: Eventual factor maps and compositions of closing maps
cites work: An Introduction to Symbolic Dynamics and Coding
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description: scientific article; zbMATH DE number 1145819