Abstract

We will show that factor codes that have a bi-closing word are bi-closing a.e. and have a degree. Moreover, a closing code with a bi-closing word into an irreducible shift space is constant-to-one. Then we study which properties may be invariant by codes that have a bi-closing word under factoring and extension. Moreover, we give some conditions for a bi-closing word and show that every closing open code in an irreducible shift space has a bi-closing word.

Keywords: Shift of finite type; sofic; synchronized; coded; closing; hyperbolic.

MSC: 37B10

DOI: 10.57016/MV-KSvK3735

Pages:  5$-$14     

Volume  76 ,  Issue  1-2 ,  2024