ON GENERALIZED CARTAN G-SPACE

In this paper. we introduce the new concept of a G-space which we call a generalized Cartan G- space . This space is weaker than a Cartan G-space which is introduced by Palais . We give the definition by depending on the definition of a generalized neighborhood which itself depends on the concept of a generalized open set which is introduced by N-Levin . We study this space and give enough examples about it . Also we study its properties ,subspace ,product and the equivariant homeomorphic image . Besides , we prove that a G-space X is a generalized Cartan G-space if X has a star thin generalized open set .