Blur shift spaces

TL;DR

This paper introduces blur shift spaces, a novel class of shift spaces that compactify classical shift spaces by representing infinite symbol sets with single symbols, extending previous isomorphism results in $C^*$-algebra theory.

Contribution

It defines and constructs blur shift spaces, generalizing prior models, and explores their use as compactifications for classical shift spaces.

Findings

Blur shift spaces generalize classical shift spaces.

They provide a compactification scheme for shift spaces.

The construction extends previous isomorphism results in $C^*$-algebra theory.

Abstract

In this work we propose a new type of shift spaces, called blur shift spaces, where one can represent with a single symbol an entire set of infinite symbols. Such shift spaces are constructed from classical shift spaces, by choosing some sets of infinitely many symbols that will be represented by a new symbol, and then defining a convenient topology. The shift spaces we are proposing generalize ideas presented previously by Ott, Tomforde and Willis, and by Gon\c{c}alves and Royer, which were used to find isomorphism between $C^*$-algebras associated to some classes of shift spaces. In particular, blur shifts can be used as a compactification scheme for classical shift spaces.