The Union of two compact sets in $\mathbb{R} ^2$ with connected complement has a connected complement
General Topology
2015-12-16 v1
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 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.
Cite
@article{arxiv.1512.04717,
title = {The Union of two compact sets in $\mathbb{R} ^2$ with connected complement has a connected complement},
author = {Yeorgios Dossidis},
journal= {arXiv preprint arXiv:1512.04717},
year = {2015}
}