# A complete classification of hereditarily equivalent plane continua

## TL;DR

This paper proves that the only non-degenerate hereditarily equivalent plane continua are the arc and the pseudo-arc, providing a complete classification of such continua in the plane.

## Contribution

It establishes a complete classification of hereditarily equivalent plane continua, showing only the arc and pseudo-arc qualify.

## Key findings

- Arc and pseudo-arc are the only non-degenerate hereditarily equivalent plane continua.
- Provides a complete classification of hereditarily equivalent plane continua.
- Clarifies the structure of hereditarily equivalent continua in the plane.

## Abstract

A continuum is hereditarily equivalent if it is homeomorphic to each of its non-degenerate sub-continua. We show in this paper that the arc and the pseudo-arc are the only non-degenerate hereditarily equivalent plane continua.