The Union of two compact sets in ℝ ² with connected complement has a connected complement

2015/12/15 by Yeorgios Dossidis, Dossidis, Yeorgios
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #General Topology (math.GN) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1512.04717

openalex publication_date 2015/12/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In the papers from Chui and Parnes (1971) and Luh (1972), as well on the paper from V.Nestoridis (1996) on the Universal Taylor series, it is used, without proof, that the union of two compact sets in ℝ ² with connected complement has a connected complement. In this work we present a rigorous proof of this fact, by studying some important topological properties of the plane.

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