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Dibyendu De and Ram Krishna Paul
Combined additive and multiplicative properties near zero view print
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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 |
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Abstract
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),⋅).
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| Acknowledgements
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.
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| Author information
Dibyendu De:
Department of Mathematics, University of Kalyani, Kalyani-741235, West Bengal, India
dibyendude@klyuniv.ac.in
Ram Krishna Paul:
Department of Mathematics, National Institute of Technology, Ravangla, South Sikkim-737139, India
rmkpaul@gmail.com
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