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Consortium for Mathematics and its Applications

Product ID: 99231
Supplementary Print
Undergraduate

The Alexander Horned Sphere (UMAP)

Author: Nelson L. Marx


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

©1977 by COMAP, Inc.
UMAP Module
14 pages

Mathematics Topics:

Geometry , Topology

Application Areas:

Prerequisites:

Parametrization of simple closed curves; topological definitions of connectedness, open and closed sets, continuous functions, and homeomorphisms

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