Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(2): 359-366

Online first article January 5, 2018      Printed March 30, 2018

https://doi.org/10.4134/BKMS.b170010

Copyright © The Korean Mathematical Society.

On closing codes

Somayyeh Jangjooye Shaldehi

Alzahra University

Abstract

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.

Keywords: shift of finite type, sofic, synchronized, coded, open, constant-to-one, hyperbolic

MSC numbers: 37B10, 54H20