Abstract
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.
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© 2004 Springer Science+Business Media New York
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Bump, D. (2004). Vector Fields. In: Lie Groups. Graduate Texts in Mathematics, vol 225. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4094-3_6
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DOI: https://doi.org/10.1007/978-1-4757-4094-3_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1937-3
Online ISBN: 978-1-4757-4094-3
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