A New SEPARATION AXIOM ii-T_(1/4)

Abstract

This research aims to continue the investigation of ii-T_(1/4) spaces, specifically their behavior when producing products. As a result, we may easily design non-ii-T_(1/4)spaces as well as ii-T_(1/4) spaces that aren'tii-T_(1/2). Furthermore, use new axioms of separation, which are, ii-T_(1/4) by using ii- open sets. We begin in section two with some definitions and theories that can be used in arriving at the new axioms of separation. Also, as an explanation of the ii-open set and some of its characteristics. We define some closed sets that explain the relationship between the new axioms of separation, including the iiλ- closed set. We also give some examples to illustrate the new axioms of separation. Furthermore, we prove its relationship to the axioms of separation.T_(1/4). We also learn about the important characteristics of these axioms. We know the new separation axioms are called ii-T_(1/4)^c spaces and clarify the relationship between them and ii-T_(1/4)space andii-T_(1/2) space. We can illustrate the relationship between the separation axioms of type ii-through a diagram and then explain and list the theorems that show the domain of products. ii-T_(1/4).