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

Authors : Sadık EYİDOĞAN, Ali Arslan ÖZKURT

Pages : 1065-1072

Doi:10.31801/cfsuasmas.901214

View : 10 | Download : 13

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :Let R R be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of R R , we will define a metric on R R 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].
Keywords : Van der Waerden Theorem, dynamical system, metric space