International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 795106, 8 pages
doi:10.1155/2011/795106
Research Article

Idealization of Some Topological Concepts

Department of Mathematics, Faculty of Science, Yarmouk University, Irbid 21163, Jordan

Received 4 December 2010; Accepted 21 March 2011

Academic Editor: Stefan Samko

Copyright © 2011 B. Al-Nashef and K. Al-Zoubi. 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 approach is followed here to generate a new topology on a set 𝑋 from an ideal and a family 𝒮 of subsets of 𝑋 . The so-obtained topology is related to other known topologies on 𝑋 . The cases treated here include the one when 𝒮 = 𝑇 𝛼 is taken, then the case when 𝒮 = 𝑅 𝑂 ( 𝑋 , 𝑇 ) is considered. The approach is open to apply to other choices of 𝒮 . As application, some known results are obtained as corollaries to those results appearing here. In the last part of this work, some ideal-continuity concepts are studied, which originate from some previously known terms and results.