On a Runge Theorem over $\mathbb{R}_3$

TL;DR

This paper explores a topological approach to the Runge theorem within the Clifford algebra R_3, focusing on the homology groups of axially symmetric open sets in the quadratic cone.

Contribution

It provides a novel topological characterization of the Runge theorem in R_3 using homology groups of specific open subsets.

Findings

Homology groups of axially symmetric open sets are key to the characterization.

A new topological perspective on the Runge theorem in Clifford algebras.

Insights into the structure of the quadratic cone in R_3.

Abstract

In this paper we investigate a topological characterization of the Runge theorem in the Clifford algebra $ \mathbb{R}_3$ via the description of the homology groups of axially symmetric open subsets of the quadratic cone in $\mathbb{R}_3$.