Door spaces on N-topology

In this article, we explore the idea of door space on -topological space. Here, we discuss which door spaces in this space are related with submaximal. The equivalent conditions shows how it connects a -topological property. Also, we derive various door spaces using separation axioms and discuss the characteristics of such door spaces. We take a strong form of open set in -topological space and introduce a new door space called - door space. In addition, we analyze -door space and discuss the relationship between a -locally closed set and -closed set