A smooth premanifold of dimension n is a Hausdorff topological space M together with a set u of pairs (U, ø), where the set of U such that (U,ø)∈ u for some ø is an open cover of M and such that, for each (U,ø) ∈ u, the image ø(U) of ø is an open subset of ℝn and ø is a homeomorphism of U onto ø(U). We assume that if U,V ∈ u, then ф v o øU −1is a diffeomorphism from (U ∩ V) onto ф V (U ∩ V). The set u is called a preatlas.
KeywordsVector Field Smooth Function Open Subset Tangent Vector Open Cover
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