Glasnik Matematicki, Vol. 41, No.1 (2006), 159-163.

ON INTERSECTION OF SIMPLY CONNECTED SETS IN THE PLANE

E. D. Tymchatyn and Vesko Valov

E. D. Tymchatyn, Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada
e-mail: tymchat@math.usask.ca

V. Valov, Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada
e-mail: veskov@nipissingu.ca

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 Repovš.

2000 Mathematics Subject Classification.   54C55, 55M15, 54F15.

Key words and phrases.   Helly theorem, plane continua, absolute retracts.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.13

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