1950-51 Expose 14. In the definition of a sheaf, X is not assumed to satisfy any separation axioms. S is called the sheaf space, π the projection map, and X the base space. The open sets of S which project homeomorphically onto open sets of X form a base for the open sets of S . Proof. If p is in an open set H, there exists an open G, p ∈ G such that π|G maps G homeomorphically onto an open set π(G). Then H ∩ G is open, p ∈ H ∩ G ⊂ H, and η|H ∩.