New York Journal of Mathematics
Volume 18 (2012) 353-360


Dibyendu De and Ram Krishna Paul

Combined additive and multiplicative properties near zero

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Published: May 28, 2012
Keywords: Algebra in the Stone-Čech compactification, Ramsey theory, Central sets near 0.
Subject: Primary 05D10; Secondary 22A15

It was proved that whenever N 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),⋅).


The first named author is partially supported by DST-PURSE programme.
The work of this article was a part of second named author's Ph.D. dissertation, which was supported by a CSIR Research Fellowship.

Author information

Dibyendu De:
Department of Mathematics, University of Kalyani, Kalyani-741235, West Bengal, India

Ram Krishna Paul:
Department of Mathematics, National Institute of Technology, Ravangla, South Sikkim-737139, India