Some Results Related to Topological Groups via Ideal Topological Spaces

An ideal on a set X is a nonempty collection of subsets of X with heredity property which is also closed finite unions. The concept of Γδ : P(X)→ τ defined as follows for every A ∈ X, Γδ(A) = {x ∈ X : there exists a U ∈ τ δ(x) such that U − A ∈ I}, was introduced by Al-Omari and Hatir [1]. In this paper, we introduce and study δ∗-homeomorphism and Γδ-homeomorphism. Also we give some application to topological groups using δ-open function and Γδ-operator. 2000 Mathematics Subject Classification: 54A05 keywords: ideal topological space, δ-open set, Γδ-operator, topological group