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 from an ideal and a family of subsets of . The so-obtained topology is related to other known topologies on . The cases treated here include the one when is taken, then the case when is considered. The approach is open to apply to other choices of . 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.