We found mathematical concepts in ideal space that led to the partitioning of space into three pairwise disjoint: * - Frontier set, disputed set and the outer function. These sets have a direct and indirect relationship to the *- resolvable and *- irresolvable spaces. Also, we put a new type of open sets, we called them IR-Open and I* R-open and the relationship of the topologies of generates with urysohn space, we also included some important results of resolvability ideal spaces.