Sheaves of Sets

This chapter starts with the notion of a sheaf F on a topological space X. Such a sheaf is a way of describing a class of functions on X- especially classes of “good” functions, such as the functions on (parts of) X which are continuous or which are differentiable. The description tells the way in which a function f defined on an open subset U of X can be restricted to functions f ∣v on open subsets V ⊂ U and then can be recovered by piecing together (collating) the restrictions to the open subsets V_i of a covering of U. This restriction-collation description applies not just to functions, but also to other mathematical structures defined “locally” on a space X.