Sheaf of continuous functions

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This article describes a sheaf on a manifold (the manifold may possess some additional structure in terms of which the sheaf is defined)
View other sheaves on manifolds


Let M be a topological manifold (or more generally, any topological space). The sheaf of continuous functions on M is defined as follows:

  • To every open subset U of M, we associate the \R-algebra of continuous real-valued functions on U
  • The restriction map is simply function restriction

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