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
• DOI: 10.4995/agt.2022.16143
• Enlaces
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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.

• Referencias bibliográficas
  • R. Arens, Topologies for Homeomorphism Groups, American Journal of Mathematics 68 (1946), 593-610. https://doi.org/10.2307/2371787
  • N. J. Fine and G. E. Schweigert, On the group of homeomorphisms of an arc, Annals of Mathematics 62 (1955), 237-253. https://doi.org/10.2307/1969678
  • M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002. https://doi.org/10.1017/CBO9780511755316
  • R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA, second...
  • I. N. Herstein, Topics in Algebra, John Wiley and Sons, 2nd Revised edition, 1975.
  • A. G. O'Farrell, Conjugacy, involutions, and reversibility for real homeomorphisms, Irish Math. Soc. Bulletin 54 (2004), 41-52. https://doi.org/10.33232/BIMS.0054.41.52
  • S. Ulam and J. von Neumann, On the group of homeomorphisms of the surface of the sphere, (abstract), Bull. Amer. Math. Soc. 53 (1947), 506.
  • J. V. Whittaker, Normal subgroups of some homeomorphism groups, Pacific J. Math. 10, no. 4 (1960), 1469-1478. https://doi.org/10.2140/pjm.1960.10.1469