English

Open maps between shift spaces

Dynamical Systems 2009-09-24 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0810.4627,
  title  = {Open maps between shift spaces},
  author = {Uijin Jung},
  journal= {arXiv preprint arXiv:0810.4627},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T11:34:53.874Z