α-local function and its properties in ideal topological spaces

In this paper, we introduce the notation of a-local function and study its properties in ideal topological space. We construct a topology тa* for X by using a-open set and an Ʈ on X. We defined a-compatible of т with ideal and show that т is a-compatible with Ʈ then тa* - β(Ʈ, т), where β(Ʈ, т) - {V-I : V € тa (x), I € Ʈ} is a basis of тa* Also, The relationships other local functions such as local function [12, 6] and semi-local function [7] are introduced.