On the retracts and recodings of continuing codes
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1375-1382
Printed July 31, 2015
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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