Generalized \(\mathcal{I}_\mathcal{p}\)-Closed Sets in Ideal Topological Spaces

The main focus of this study is to introduce a new category of generalized closed sets, referred to as
- closed sets, within the framework of ideal topological spaces. By using a few instances, we demonstrate
- closed sets and establish some fundamental properties of
-closed sets. We also investigate the relationship between
-closed sets and other classes of generalized closed sets in ideal topological spaces, such as (\mathcal{I}_\mathcal{g}\)- closed sets,
-closed sets, and (\mathcal{I}_\mathcal{r}\)\mathcal{g}\)-closed sets. Then, we focus on the topological implications of
-closed sets and investigate how they relate to the concepts of
-continuous map, (\mathcal{I}_\mathcal{p}\)-irresolute map, and a strongly
-continuous map. First and foremost, we define the
-continuous map, investigate the behavior of
- continuous map with respect to
-closed sets, and derive several important properties of
-continuous map. Further, we studied their relationships with other classes of continuous maps in ideal topological spaces. Nevertheless, we defined the definitions of
-irresolute maps and strongly
-continuous maps in ideal topological spaces. We explored the connections with the notions of
-continuous map, (\mathcal{I}_\mathcal{p}\)-irresolute map, and a strongly
-continuous map. Our results provide new insights into the study of ideal topological spaces.