On Runge Pairs and topology of axially symmetric domains

TL;DR

This paper establishes a Runge theorem for axially symmetric open subsets of the quaternions and explores their homological properties, advancing understanding in complex analysis and topology.

Contribution

It introduces a Runge theorem tailored for axially symmetric domains in quaternions and analyzes their homology, a novel combination in this context.

Findings

Proved a Runge theorem for axially symmetric domains

Described the homology of these domains

Enhanced understanding of their topological properties

Abstract

We prove a Runge theorem for and describe the homology of axially symmetric open subsets of H.