On Generalized Dispersive G-spaces

In this paper we introduce a new G-space which we call a generalized dispersive G-space. This space is weaker than a dispersive G-space which is introduced in [2] and stronger than a generalized cartan G-space which is introduced in (3]. We give the definition by depending on the defenition of a generalized neighborhood which itself depends on the concept of a generalized open set which is introduced by N-Levin (6]. We study this space and give enough examples about it. Also we study its properties subspace, product space and the equivariant homeomorphic image. Finally we prove that a G-space X is a generalized dispersive G-space if X has a star thin generalized open set