ABSTRACT
The purpose of the above-mentioned research article gives an explanation of the new notions of interior and closure of a set, which are referred to as s*p* interior set and s*p* closure set, utilizing the closed set and open set of s* p* and to discuss certain fundamental aspects of the s* p* closure set and s* p* interior set in a topological space. The inner and outer edges of a set were introduced by many researchers. The inner of a topological set is the connection of all open subsets. The interior is the closure's complement. That is, the interior and closure are complementary. In addition, the ideas of s*p* neighbourhood and s*p* derived sets by going over a number of theorems related to this concept. The ideas of open set and interior are intimately tied to the idea of neighbourhood. The neighbourhood system refers to the totality of all neighbourhoods. Georg cantor was the first to present the ideas of derived set in 1872. Therefore, the derived set is defined as the collection of all accumulation points.
