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

It is known that for an IP* set in ？ and a sequence ？？∞=1 there exists a sum subsystem ？？∞=1 of ？？∞=1 such that (？？∞=1)∪(？？∞=1)？. 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,∞),