Study of Hpre-open sets in topological spaces

The concept main of paper is to connected between two definitions pre-open sets and g-open sets in the topological spaces is called Hpre-open sets, study restudy relations them, also present a new definitions, namely Hpre-continous, Hpre-open functions, Hpre-closed functions and have proved some theorems about these concept. Finally, we have present the definitions and results of separation axioms by Hpre-open sets,namely Hpre - T1 spaces , Hpre - T2 spaces and studied some of its applications.