Let X be a connected and locally path connected topological space. Constructing the sheaf of homology groups över X, its some characterizations are given. Furthermore, defining the Generalized Whitney Sum and Direct Sum of the sheaves and H2 , it is shown that the sheaf (H) = H \® H ı is isomorphic to the sheaf Hı x Hı. Where, 77 ı and H ı are sheaves of homology groups över X{ and X2, respectively.