On Unions and Intersections of Simply Connected Planar Sets

• Autores: Umed H. Karimov, Dusan Repovs, Matjaz Zeljko
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 145, Nº 3, 2005, págs. 239-245
• Idioma: inglés
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• Resumen

  • We construct several simple examples of planar compacta which show that without additional conditions, a theorem of Breen and a direct generalization of the Seifert-van Kampen theorem fail. We give answers to two conjectures of Bogatyi and a partial solution to his third conjecture. We give a counterexample to a statement in the classical survey paper by Danzer¿Grünbaum¿Klee, related to Molnár¿s result on intersections of simply connected planar sets