Abstract
In this chapter we develop analytic tools that will be fundamental to our study of manifolds. Partitions of unity (section 3.2) are the most important of these tools, but to prove their existence (3.2.4) we need to impose some restrictions on our manifolds (3.1.6); we provide some motivation for this step in section 3.1.
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© 1988 Springer Science+Business Media New York
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Berger, M., Gostiaux, B. (1988). Partitions of Unity, Densities and Curves. In: Differential Geometry: Manifolds, Curves, and Surfaces. Graduate Texts in Mathematics, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1033-7_4
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DOI: https://doi.org/10.1007/978-1-4612-1033-7_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6992-2
Online ISBN: 978-1-4612-1033-7
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