Combined Algebraic Properties of IP* and Central* Sets Near 0Report as inadecuate




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International Journal of Mathematics and Mathematical SciencesVolume 2012 2012, Article ID 830718, 7 pages

Research Article

Department of Mathematics, University of Kalyani, West Bengal, Kalyani 741235, India

Department of Mathematics, National Institute of Technology, South Sikkim, Ravangla 737139, India

Received 25 March 2012; Accepted 26 June 2012

Academic Editor: Manfred Moller

Copyright © 2012 Dibyendu De and Ram Krishna Paul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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,∞,+.





Author: Dibyendu De and Ram Krishna Paul

Source: https://www.hindawi.com/



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