In the context of sheaf theory in mathematics, a **constant sheaf** is a particular type of sheaf that assigns the same set (or space) to every open set of a topological space, while also encoding the necessary gluing and restriction properties of sheaves.
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For an abelian group , the constant sheaf has sections over an open set given by its locally constant -valued functions. It is the sheafification of the constant presheaf, and its sections on a disconnected open set need not have a single common value.