Combined Algebraic Properties of IP* and Central* Sets Near 0

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* sets. In this present work we will extend the results for dense subsemigroups of ((0,∞),+)