Lie Rough Groups

Abstract

This paper introduces the definition of a Lie rough group as a natural development of the concepts of a smooth manifold and a rough group on a approximation space. Furthermore, the properties of Lie rough groups are discussed. It is shown that every Lie rough group is a topological rough group, and that the product of two Lie rough groups is again a Lie rough group. We define the concepts of Lie rough
subgroups and Lie rough normal subgroups. Finally, we aim is to give an example by using definition of Lie rough homomorphism sets G and H.