Partitions of Unity, Densities and Curves
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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.
KeywordsVector Field Open Cover Compact Manifold Measure Zero Integral Curve
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