On real polynomial local homeomorphisms

TL;DR

This paper proves that for polynomial mappings in three-dimensional space that are local homeomorphisms, the set where they are not proper cannot be topologically equivalent to a real line.

Contribution

It establishes a topological restriction on the non-properness set of such polynomial local homeomorphisms in three dimensions.

Findings

Non-properness set cannot be homeomorphic to a real line.

Provides new constraints on polynomial local homeomorphisms in 3D.

Advances understanding of polynomial mapping topology.

Abstract

We prove that the set of non-properness of a polynomial mapping of the three dimensional space which is a local homeomorphism cannot be homeomorphic to the real line $\R.$