On-iαw – Closed-Sets and -iαw – Continuous Functions

Abstract

The first goal in this essay will explain the notation of iαw- closed sets and iαw- open sets in topological space. Many properties and relationships among those sets are investigated. We also discovered that there is no relationship between iαw- closed sets and α- closed, i- closed, iα- closed sets. Additionally, we start by teaching the ideas of , prefectly, , and obtain the basic properties. Also, we prove that each in any topological space is in any topological space is and there is no relationship between as well as some of its features. Finally, we concluded that every it is , every continuous iscontinuous and every continuous function is.

Keywords

• iαw- closed set
• iw- closed set
• iαw- continuous function
• iw- continuous function
• w- continuous function