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Chinese Journal of Mathematics
Volume 2013 (2013), Article ID 973608, 6 pages
http://dx.doi.org/10.1155/2013/973608
Research Article

Some New Sets and Topologies in Ideal Topological Spaces

1Department of Mathematics, Sathyabama University, Chennai, Tamil Nadu 600119, India
2Department of Mathematics, Karunya University, Coimbatore, Tamil Nadu 641114, India

Received 30 July 2013; Accepted 16 September 2013

Academic Editors: Y. Fu and C. Wang

Copyright © 2013 R. Manoharan and P. Thangavelu. 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

An ideal topological space is a triplet ( , , ), where is a nonempty set, is a topology on , and is an ideal of subsets of . In this paper, we introduce -perfect, -perfect, and -perfect sets in ideal spaces and study their properties. We obtained a characterization for compatible ideals via -perfect sets. Also, we obtain a generalized topology via ideals which is finer than using -perfect sets on a finite set.