Some results on the sheaf of the homology groups

Abstract

Let X be a connected and locally path connected topological space. Constructing the sheaf of homology groups over X, its some characterizations are given. Furthermore, defining the Generalized Whitney Sum and Direct Sum of the sheaves $overline H_1$ and $overline H_2$ , it is shown that the sheaf $(overline H)^ast =overline H_1bigoplusoverline H_2$ is isomorphic to the sheaf $overline H_1x overline H_2$ Where, $overline H_1$ and $overline H_2$ are sheaves of homology groups over X1 and X2, respectively.