On the image set and reversibility of shift morphisms over discrete alphabets

TL;DR

This paper establishes conditions under which the image of a shift-commuting map over a discrete alphabet remains a shift space and shows that injective such maps have continuous, shift-commuting inverses.

Contribution

It provides new sufficient conditions for the image of a shift-commuting map to be a shift space and characterizes the reversibility of injective maps.

Findings

Image of a continuous shift-commuting map is a shift space under certain conditions

Injective shift-commuting maps have continuous, shift-commuting inverses

Conditions applicable to arbitrary discrete alphabets

Abstract

In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is injective, then its inverse is also continuous and shift-commuting.