<b>On <i>R</i><sub>1</sub>- Separation Axioms</b>

The purpose of this research is to present the new set that is named open set, where the set was defined and the general properties And the basic concepts and properties of the set were explained, such as the open set, the intersection, and the union. also In this paper the separation axioms were defined and studied in ideal topological spaces in a new way. and discuss some properties. Also discuss the relationship of our definition with other definitions and prove some results in the context of separation axioms in ideal topological space on this set, where the axioms of the type - space, -space and – space were defined and the basic concepts and generalizations of these axioms on the set were studied. In addition the relationships between these concepts and their converses on this set under study were discussed, and illustrative examples and proofs of those properties were provided for that. Additionally, a diagram illustrating these concepts is presented