Homeomorphisms on compact metric spaces with finite derived length

V. Kannan, Sharan Gopal

Abstract

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.


Keywords

ordinal; homeomorphism; periodic point

Subject classification

06A99; 54H20

Full Text:

PDF

References

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

Abstract Views

1733
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt