Uncountably many planar embeddings of unimodal inverse limit spaces

TL;DR

This paper constructs uncountably many planar embeddings of unimodal inverse limit spaces, demonstrating that each embedding can make a specific point accessible, using symbolic dynamics techniques.

Contribution

It introduces a method to generate uncountably many non-equivalent planar embeddings of unimodal inverse limit spaces with accessible points.

Findings

Uncountably many non-equivalent planar embeddings exist for these spaces.

Each embedding can be constructed to make a chosen point accessible.

The method employs symbolic dynamics for embedding construction.

Abstract

For point $x$ in the inverse limit space $X$ with a single unimodal bonding map we construct, with the use of symbolic dynamics, a planar embedding such that $x$ is accessible. It follows that there are uncountably many non-equivalent planar embeddings of $X$.