Topological Factors of Rank-One Subshifts

TL;DR

This paper characterizes the subshift factors of rank-one subshifts, showing they are either finite or isomorphic to the original, thus providing a complete classification of such factors.

Contribution

It provides a complete characterization of subshift factors of rank-one subshifts, identifying their possible forms.

Findings

Subshift factors are either finite or isomorphic to the original rank-one subshift.

The classification of subshift factors is complete and definitive.

The results deepen understanding of the structure of rank-one subshifts.

Abstract

We study topological factors of rank-one subshifts and prove that those factors that are themselves subshifts are either finite or isomorphic to the original rank-one subshifts. Thus, we completely characterize the subshift factors of rank-one subshifts.