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On intersection of simply connected sets in the plane

E. D. Tymchatyn·V. Valov
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Abstract

Several authors have recently attempted to show that the intersection of three simply connected subcontinua of the plane is simply connected provided it is non-empty and the intersection of each two of the continua is path connected. In this note we give a very short complete proof of this fact. We also confirm a related conjecture of Karimov and Repovs.

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E. D. Tymchatyn, V. Valov. 2005-01-03. On intersection of simply connected sets in the plane. https://arxiv.org/abs/math/0409349

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