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In this paper, we use  the definition of the action on the set of semi-group of the structure of this research .We introduce the concepts of  -system which is a triple , ,  such that  is a Hausdorff compact space called  phase space,  is a semi-group of transformations with a continuous action  of   on  . We study and proof some theoretical properties related with that system. We also introduce the concept of Enfolding semi-group ( , ,and we prove that it is a compact right topological semi-group. In addition, we study the left and right ideals in the Enfolding semi-group. By using the dynamical system, we reflect various properties concerning with its structure for the Enfolding semi-group. Furthermore, we describe the connections between the algebraic and topological properties of the Enfolding semi-group space.

In the present paper, a comparison  between classical masks and (odd and even) masks groups for Mycosis Fungoides disease Skin image edges detection is performed.The goal is to extract the information known in the image because it is vital to understand the image content as the proposed approach is the comparative edge by masks classical and a new set  of Groups  masks (odd and even ) which consist of 10 masks. The  database consists of 40 images reprints different  stage of the Mycosis Fungoides disease Skin images 10 images for each stage. The experimental results confirm the effectiveness of the proposed system. and confirm the effectiveness of the proposed(odd and even) Groups masks.