A note on strong Jordan separation

TL;DR

This paper extends Jordan separation theorems to more general settings where the domain is a compact topological space, not necessarily a sphere, and the map may not be injective, broadening the theorem's applicability.

Contribution

It strengthens Jordan separation results for maps from arbitrary compact spaces into spheres, relaxing previous assumptions about injectivity and domain shape.

Findings

Generalized Jordan separation for non-injective maps

Applicable to broader classes of topological spaces

Enhanced understanding of topological embeddings

Abstract

We provide a strengthening of Jordan separation, to the setting of maps from a compact topological space X into a sphere, where the source space X is not necessarily a codimension one sphere, and the map is not necessarily injective.