Open maps between shift spaces

Details Open maps between shift spaces Open maps between shift spaces

2008-10-25

arxiv.org/abs/0810.4627v1

Ergodic Theory and Dynamical Systems (2009), 29 (4):1257-1272

Mathematics

Dynamical Systems

16 pages, 3 figures; to appear in Ergodic Theory Dynamical Systems

Scientific paper

10.1017/S0143385708000692

Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions -- open, constant-to-one, (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.

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