$ii \delta_g$-closed set in topological spaces

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Pure Science, Wassit University, Iraq

Abstract

The purpose of this study is to determine if it is possible to use the class of $\delta_g-$close sets and $\delta-$closed sets to find a new class of close sets, namely $ii\delta_g-$close sets and $ii\delta-$close sets. We use these new classes to arrive at the separation axiom, which is the separation axiom of $ii-T_{3/4}.$  We also use the properties of $\delta \hat{g}-$closed sets to find new class of close sets, namely $ii\delta \hat{g}-$closed set. We use it to create a new type of separation axiom. The study found new closed sets, namely: $ii\delta \hat{g}-$closed sets is introduced for topological space. We will also prove that category falls between the class of $ii\delta-$closed set and the class of $iigs-$closed set. As well study the relationship between it and other closed sets, such as the closed set of type $iigs-$ as well as the closed set of type $iig$, and then, through these closed sets, we will study new types of the axiom of separation, which are $ ii- T_{3/4}$ space and $ ii- \hat{T}_{3/4}$ space, and also clarify the relationship between the axiom of separation, and some of the closed and open sets previously studied. The study also included the relationship between the axiom of separation, of type $ii-T_{1/2}$ space and $ii- T_{3/4}$ space as well as the axiom of separation of type  $ii- T_{3/4}$ space and $ ii \hat{T}_{3/4}$ space. The study included some important proofs. The study also included a chart, showing the relationship between closed sets of types that were studied and can be used.

Keywords