The Alexander Horned Sphere (UMAP)

A unit that involves applications of introductory topology. The purpose of this module is for students to: 1) understand the construction of the Alexander horned sphere; and 2) discover properties of the horned sphere as a counterexample to Shoenfliess Theorem for the standard sphere.

Table of Contents:

1. INTRODUCTION

2. THE JORDAN CURVE AND SHOENFLIESS THEOREMS

3. THE HORNED SPHERE

4. SIMPLY CONNECTED SETS

5. THE EXTERIOR OF THE HORNED SPHERE

6. PROBLEM

SOLUTION