On real polynomial local homeomorphisms
Alexandre Fernandes, Zbigniew Jelonek

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
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions · Mathematical Dynamics and Fractals
