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Open maps between shift spaces

Published online by Cambridge University Press:  01 August 2009

UIJIN JUNG
UIJIN JUNG*
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 305-701, Korea (email: [email protected])
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Abstract

Given a code from a shift space to an irreducible sofic shift, any two of the three conditions—open, constant-to-one and (right or left) closing—imply the third. If the range is not sofic, then the same result holds when bi-closingness replaces closingness. Properties of open mappings between shift spaces are investigated in detail. In particular, we show that a closing open (or constant-to-one) extension preserves the structure of a sofic shift.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1257 - 1272
Copyright
Copyright © Cambridge University Press 2009

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