Inverse limits with countably Markov interval functions

TL;DR

This paper introduces countably Markov interval functions and demonstrates that inverse limits with such bonding functions are homeomorphic if they follow the same pattern, generalizing previous results.

Contribution

It generalizes existing results by establishing homeomorphism conditions for inverse limits with countably Markov interval functions.

Findings

Inverse limits with countably Markov interval functions are homeomorphic if they follow the same pattern.

Generalization of previous results by Holte, Banic, and Lunder.

Provides a new framework for understanding inverse limits with countably Markov functions.

Abstract

We introduce countably Markov interval functions and show that two inverse limits with countably Markov interval bonding functions are homeomorphic if the functions follow the same pattern. This result presents a generalization of well-known results of S. Holte, and I. Bani\v{c} and T. Lunder.