Using ideals defined, on a set many new sets and topologies were defined by many authors. We define a new set (τI- mini open set) in ideal space with the use of an ideal and later we proved the collection of that new sets has the properties of generating a new topology which we named as introduce a new topology called τI- topology which is containing the actual topology τ.
Some new sets like of "R * -LC-sets", "R * -I-LC-sets" are introduced using R * -topology. Also defined the notions of "R * -I-LCcontinuous maps", "I * R -continuous maps", "g-R * -continuous map"s and represent "*-continuous function" as decomposition two newly defined functions.
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