differential structure

First let (M,𝜏) be a topological space. The sheaf 𝔊 of real continuous functions on (M,𝜏) is said to be a differential structure on M if for any open set U∈𝜏, any functions f_i∈𝔊(U), and any w∈C ᪲(ℝⁿ), the superposition w∘(f_1,…f_n)∈𝔊(U).