On the group of homeomorphisms on R: A revisit

• Ali Akbar, Kamaludheen ^[1] ; Mubeena, T. ^[2]
  1. [1] Central University of Kerala

     Central University of Kerala

     India

     
  2. [2] University of Calicut

     University of Calicut

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 2, 2022, págs. 269-280
• Idioma: inglés
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• Resumen

  •  In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R ([2], [6], [7] and [8]), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.