Set operators and associated functions

Abstract

The study of two operators local function and the set operator $\psi$ on the ideal topological spaces are likely to be same to the study of closure and interior operator of the topological spaces. However, they are not exactly equal with the interior and closure operator of the topological spaces. In this context, we introduce two new set operators on the ideal topological spaces. Detail properties of these two operators are the part of this article. Furthermore, the operators interior (resp. $\psi$) and closure (local function) obey the relation $Int(A)$= X \ $Cl$(X \ A) (resp. $\psi$(A) = X \(X \A)$^*)$. We search the general method of these relations, through this manuscript.

Keywords

• local function
• associated function
• $\psi_M$ operator
• $\psi$ operator

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