On the group of homeomorphisms on R: A revisit


  • Kamaludheen Ali Akbar Central University of Kerala
  • T. Mubeena University of Calicut




Group of homeomorphisms, Normal subgroups, Dynamical systems, Fixed points, Conjugacy, bounded functions


 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.


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Author Biographies

Kamaludheen Ali Akbar, Central University of Kerala

Department of Mathematics, School of Physical Sciences

T. Mubeena, University of Calicut

Department of Mathematics, School of Mathematics and Computational Science


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How to Cite

K. Ali Akbar and T. Mubeena, “On the group of homeomorphisms on R: A revisit”, Appl. Gen. Topol., vol. 23, no. 2, pp. 269–280, Oct. 2022.



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