On ici-Open Sets in Topological Spaces

Abstract

A new concept in topological space called ici-open set is introduced, depended on the common adjective between i-open and int-open sets. Therefore, every ici-open set is i-open and int-open set. The ici-open sets inherits some properties from i-open and int-open sets, as every ici-open set is a semi-open set. The family of i-open sets forms a topological space if it generated from topology contains just three elements, the third element is set with one element but when contain more than one that is not true. This case has different behavior for the family of ici-open sets, which forms a topological space even if the mention set contains more than one element. In addition, some properties and theorems using ici-open sets have been proved.