Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(4): 1375-1382

Printed July 31, 2015

https://doi.org/10.4134/BKMS.2015.52.4.1375

Copyright © The Korean Mathematical Society.

On the retracts and recodings of continuing codes

Jisang Yoo

Ajou University

Abstract

We investigate what happens when we try to work with continuing block codes (i.e., left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on strictly sofic shifts do not behave as well as those on shifts of finite type; a continuing block code on a sofic shift need not have a uniformly bounded retract, unlike one on a shift of finite type. A right eresolving code on a sofic shift can display any behavior arbitrary block codes can have. We also show that a right continuing factor of a shift of finite type is always a shift of finite type.

Keywords: eresolving, right continuing code, infinite-to-one code, SFT, factor map

MSC numbers: Primary 37B10

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