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arXiv · 1902.09622

D-sets in Arbitrary Semigroup

Surajit Biswas·Bedanta Bose·Sourav Kanti Patra
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Abstract

We define the notion of $D$-set in an arbitrary semigroup, and with some mild restrictions we establish its dynamical and combinatorial characterizations. Assuming a weak form of cancellation in semigroups we have shown that the Cartesian product of finitely many $D$-sets is a $D$-set. A similar partial result has been proved for Cartesian product of infinitely many $D$-sets. Finally, in a commutative semigroup we deduce that $D$-sets (with respect to a F{\o}lner net) are $C$-sets.

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Surajit Biswas, Bedanta Bose, Sourav Kanti Patra. 2019-02-14. D-sets in Arbitrary Semigroup. https://doi.org/10.1016/j.topol.2020.107329

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