Combined algebraic properties of C∗ -sets near zero
It is known that for an IP∗ set A in N and a sequence ⟨xn⟩n=1∞ there exists a sum subsystem ⟨yn⟩n=1∞ of ⟨xn⟩n=1∞ such that FS(⟨yn⟩n=1∞)∪ FP(⟨yn⟩n=1∞)⊆A. Similar types of results also have been proved for central∗ and C∗-sets where the sequences considered belong to a restricted class of sequences. In 2012, D. De and R. K. Paul have extended these results for IP∗ and central∗ sets near zero in dense subsemigroups of ((0 , ∞) , +). In this present work we will extend the results for C∗-sets near zero in dense subsemigroups of ((0 , ∞) , +).
Bhattacharya, Tanumoy; Chakraborty, Sukrit; and Patra, Sourav Kanti, "Combined algebraic properties of C∗ -sets near zero" (2020). Journal Articles. 291.