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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 2 | Year 2019 | Article Id. IJMTT-V65I2P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I2P502

An Approach to Van Der Waerden’s Theorem using Topological Dynamics


Mdi B Jeelani Shaikh, J B Anasuya
Abstract

The motivation involved in doing this paper is understanding Ramsey theory in a better way.In this paper a detailed study of topological dynamics in Ramsey theory is made,which is then used to make an appropriate approach to Van der waerdan’s theorem.We will start by using some basics in topological dynamics.

Keywords
Vanderwaeden theorem, Topological space, Ramsey theory
References

[1] V.Bergelson, Ergodic Ramsy theory – an update, Ergodic Theory of Zd - actions. M.Poilicott and K. Schmidt, editors, London Mathematical Society Lecture Notes Series 228 (1996) 1-61.j135 V. Bergelson,Ergodic theory and Diophantine problems, Symbol. Dynamics and its Applications, F. Blanchard, R. Nogueira and A. Maass. eds. Cambridge University Press. 1999.
[2] V.Bergelson and N. Hindman. Nonrnetrizable topological dynamics and Ramsey theory. Trans. Amer. Math. Soc. 320 (1990) 293-320.
[3] A.Blaszczyk. S. Piewik, and S. Turek. Topological multidimensional van der Waerden theorem, Comment. Math. Univ. Carotin. 30 (1989) 783-787.
[4] Elemental methods in ergodic ramsey theory,Randall McCutcheon.1722,[6-12].
[5] H.furstenberg ,B.weiss ,Topological dynamicsand combinatorial theory,J.d’Analyse math .34(1978),61-85.
[6] R.Graham,B.rothschild and J.pencer,Ramsey theory,new York,1980.
[7] B.L.van der Waerden, BeweiseinerBaudetschenVermutung, Nieuw Arch. wisk 15 (1927) 212-216.

Citation :

Mdi B Jeelani Shaikh, J B Anasuya, "An Approach to Van Der Waerden’s Theorem using Topological Dynamics," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 2, pp. 6-9, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I2P502

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