Idealization of Some Topological Concepts

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.