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On the group of homeomorphisms on R: A revisit

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On the group of homeomorphisms on R: A revisit

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Ali Akbar, K.; Mubeena, T. (2022). On the group of homeomorphisms on R: A revisit. Applied General Topology. 23(2):269-280. https://doi.org/10.4995/agt.2022.16143

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Título: On the group of homeomorphisms on R: A revisit
Autor: Ali Akbar, Kamaludheen Mubeena, T.
Fecha difusión:
Resumen:
[EN]  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 ...[+]
Palabras clave: Group of homeomorphisms , Normal subgroups , Dynamical systems , Fixed points , Conjugacy , Bounded functions
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2022.16143
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2022.16143
Código del Proyecto:
info:eu-repo/grantAgreement/UOC//11733%2F2021
info:eu-repo/grantAgreement/SERB/MTR%2F2018%2F000256
Agradecimientos:
The first author acknowledges SERB-MATRICS Grant No. MTR/2018/000256 for financial support. The second author acknowledges University of Calicut, Seed Money (U.O. No. 11733/2021/Admn; Dated: 11.10.2021), INDIA for financial ...[+]
Tipo: Artículo

References

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. 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 edition, 1989.

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

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