D-sets in Arbitrary Semigroup

DOI10.1016/J.TOPOL.2020.107329arXiv1902.09622MaRDI QIDQ6314615

Surajit Biswas, Bedanta Bose, Sourav Kanti Patra

Publication date: 14 February 2019

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.

Mathematics Subject Classification ID

Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Ramsey theory (05D10) Semigroups (20M99) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

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