Arcs, hypercubes, and graphs as quotients of projective Fra\"iss\'e limits

TL;DR

This paper explores how various compact metric spaces, including arcs, hypercubes, and graphs, can be represented as quotients of projective Fra"issé limits, expanding understanding of their structural properties.

Contribution

It demonstrates that arcs, hypercubes, and graphs can be realized as quotients of projective Fra"issé limits within a finite language, providing new insights into their construction.

Findings

Arcs are directly shown to be quotients of projective Fra"issé limits.

Hypercubes and graphs are obtained via closure properties of these limits.

The paper establishes foundational properties of these quotient spaces.

Abstract

We establish some basic properties of quotients of projective Fra\"iss\'e limits and exhibit some classes of compact metric spaces that are the quotient of a projective Fra\"iss\'e limit of a projective Fra\"iss\'e family in a finite language. We prove the result for the arcs directly, and by applying some closure properties we obtain all hypercubes and graphs as well.