The aim of this paper is to introduce the notation of pre-local function A
p
∗
(I, τ) by using preopen 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.
