Topologically mixing extensions of endomorphisms on Polish groups

• Burke, John ^[1] ; Pinheiro, Leonardo ^[1]
  1. [1] Rhode Island College

     Rhode Island College

     City of Providence, Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 1, 2022, págs. 179-187
• Idioma: inglés
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• Resumen

  • In this paper we study the dynamics of continuous endomorphisms on Polish groups. We offer necessary and sufficient conditions for a continuous endomorphism on a Polish group to be weakly mixing. We prove that any continuous endomorphism of an abelian Polish group can be extended in a natural way to a topologically mixing endomorphism on the countable infinite product of said group.