Homeomorphisms on compact metric spaces with finite derived length


  • V. Kannan University of Hyderabad
  • Sharan Gopal Birla Institute of Technology and Science - Pilani




ordinal, homeomorphism, periodic point


The sets of periodic points of self homeomorphisms on an ordinal of finite derived length are characterised, thus characterising the same for homeomorphisms on compact metric spaces with finite derived length. A partition of ordinal is introduced to study this problem which is also used to solve two more problems: one about an equivalence relation and the other about a group action, both on an ordinal of finite derived length.


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Author Biographies

V. Kannan, University of Hyderabad


School of Mathematics and Statistics

Sharan Gopal, Birla Institute of Technology and Science - Pilani

Assistant Professor.

Department of Mathematics


I. N. Baker, Fixpoints of polynomials and rational functions, J. London Math. Soc. 39 (1964), 615-622. https://doi.org/10.1112/jlms/s1-39.1.615

P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic abstract Algebra, Second Edition, Cambridge University Press, 1995. https://doi.org/10.1017/CBO9781139174237

J. P. Delahaye, The set of periodic points, Amer. Math. Monthly 88 (1981), 646-651. https://doi.org/10.1080/00029890.1981.11995336

B. J. Gardener and M. Jackson, The Kuratowski Closure-Complementation theorem, New Zealand Journal of Mathematics, 38 (2008), 9-44.

K. H. Hofmann, Introduction to topological groups, an introductory course (2005).

V. Kannan, A note on countable compact spaces, Publicationes Mathematicae Debrecen 21 (1974), 113-114.

J. L.Kelley, General Topology, Graduate Texts in Mathematics-27, Springer, 1975.

S. Mazurkiewicz and W.Sierpinski, Contribution a la topologie des ensembles denombrables, Fund. Math 1 (1920), 17-27. https://doi.org/10.4064/fm-1-1-17-27

G. Polya and R. C. Read, Combinatorial enumeration of groups, graphs, and chemical compounds, Springer-Verlag, New York, 1987. https://doi.org/10.1007/978-1-4612-4664-0

S. M. Srivastava, A course on Borel sets, Graduate Texts in Mathematics-180, Springer, 1998. https://doi.org/10.1007/978-3-642-85473-6

S. Gopal and C. R. E. Raja, Periodic points of solenoidal automorphisms, Topology Proceedings 50 (2017), 49-57.

I. Subramania Pillai, K. Ali Akbar, V. Kannan and B. Sankararao, Sets of all periodic points of a toral automorphism, J. Math. Anal. Appl. 366 (2010), 367-371. https://doi.org/10.1016/j.jmaa.2009.12.032




How to Cite

V. Kannan and S. Gopal, “Homeomorphisms on compact metric spaces with finite derived length”, Appl. Gen. Topol., vol. 17, no. 2, pp. 129–137, Oct. 2016.