Fixed point free homeomorphisms of the complex plane

2016/08/09 by Nikolaos E. Sofronidis, Sofronidis, Nikolaos E.
Mathematics · #03E15 #37E30 #57S05 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Logic (math.LO) #Mathematical Dynamics and Fractals #math.GN #math.LO #msc:03E15 #msc:37E30 #msc:57S05

paper · pdf · doi:10.48550/arxiv.1608.02935

arxiv created 2016/08/09 · openalex publication_date 2016/08/09 · arxiv updated 2016/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our purpose in this article is to prove that the group H(\bf C) of homeomorphisms of the complex plane \bf C is a metric group equipped with the metric induced by uniform convergence of homeomorphisms and their inverses on compacts and the set \ h ∈ H(\bf C) : ( ∀ z ∈ \bf C )( h(z) ≠ z ) \ of fixed point free homeomorphisms of the complex plane is a conjugacy invariant dense G_δ subset of H(\bf C).

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