Abstract
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 Vi 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.
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© 1994 Springer Science+Business Media New York
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Mac Lane, S., Moerdijk, I. (1994). Sheaves of Sets. In: Sheaves in Geometry and Logic. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0927-0_4
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DOI: https://doi.org/10.1007/978-1-4612-0927-0_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97710-2
Online ISBN: 978-1-4612-0927-0
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