• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1375-1382
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• 2015

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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.359-366
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• 2018

We extend Jung's result about the relations among bi-closing, open and constant-to-one codes between general shift spaces to closing codes. We also show that any closing factor code ${\varphi}:X{\rightarrow}Y$ has a degree d, and it is proved that d is the minimal number of preimages of points in Y. Some other properties of closing codes are provided. Then, we show that any closing factor code is hyperbolic. This enables us to determine some shift spaces which preserved by closing codes.