## Abstract :

The aim of this paper is to introduce the notation of pre-local function A^(p^* )(I, τ) by using pre-open sets in an ideal topological space (X, τ, I). Some properties and characterizations of a pre-local function are explored Pre-compatible spaces are also defined and investigated. Moreover, by using A^(p^* )(I, τ) we introduce an operator ψ: P(X)→τ satisfying ψ(A) = X-〖(X-A)〗^(p^* )for each A ∈ P(X) and we discuss some characterizations this operator by use pre-open sets.