De, D.Paul, R.K.2020-03-312020-03-312012New York Journal of Mathematics, 2012, Vol.18, , pp.353-360https://idr.nitk.ac.in/handle/123456789/10250It was proved that whenever ? is partitioned into finitely many cells, one cell must contain arbitrary length geo-arithmetic progressions. It was also proved that arithmetic and geometric progressions can be nicely intertwined in one cell of partition, whenever N is partitioned into finitely many cells. In this article we prove that similar types of results also hold near zero for some suitable dense subsemigroups S of ((0,?),+) for which S?(0,1) is a subsemigroup of ((0,1), middot;).Article