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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Cilt: 70 - Sayı: 2

A variant of the proof of Van der Waerden's theorem by Furstenberg

Sadık EYİDOĞAN
Ali Arslan ÖZKURT
Sayfa
1065–1072
Yayın Tarihi
2021-12-31
DOI
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Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let RR be a commutative ring with identity.
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Temel Bulgular & Veri:In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of RR, we will define a metric on RR using them.
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Sonuç & Katkı:Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Van der Waerden Theorem · dynamical system · metric space

Abstract

Let RR be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of RR, we will define a metric on RR using them. Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].

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Bu Makaleye Atıf Yap

EYİDOĞAN, S., ÖZKURT, A. A. (2021). A variant of the proof of Van der Waerden's theorem by Furstenberg. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 70 - Sayı: 2, 1065–1072. https://ajindex.com/articles/746720

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Kaynakça (7)

  1. Birkhoff, G.D., Dynamical Systems, Math. Soc. Coll. Publ., vol 9, Amer. Math. Soc., Providence RI, 1927. https://doi.org/http://dx.doi.org/10.1090/coll/009
  2. Engelking, R., General Topology, Second Edition,
  3. Heldermann Verlag, Berlin, 1989.
  4. Furstenberg, H., Poincare recurrence and number theory, Bull. of the A. Math. Soc., 5 (3) (1981), 211–234.
  5. Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number, Princeton University Press,
  6. Princeton, New Jersey, 1981.
  7. Van der Waerden, B.L., Beweis einer baudetschen vermutung, Nieuw Arch. Wisk., 15 (1927), 212–216.