Density and invariant means in left amenable locally compact topological groups

Amenable groups have a close relationship with various mathematical concepts. In this paper we consider the correlation between the amenability and semigroup compactification of a locally compact group. It is observed that in the case that G is an amenable group, there are some wonderful properties for GLUC. Motivated by the definition provided by N. Hindman and D. Strauss, we defined the set LIM0(G) and other sets such as Φ(G) and Δ⁎(G) to achieve the desired results and we considered the correlation between the amenability and semigroup compactification of a locally compact group.