| 1. | This can be done globally, using a partition of unity.
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| 2. | The Lanczos kernel does not have the partition of unity property.
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| 3. | Every normal space admits a partition of unity.
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| 4. | This can be seen from the partition of unity property of the basis functions.
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| 5. | The partition of unity allows us to construct a set of continuous functions such that
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| 6. | Partitions of unity are useful because they often allow one to extend local constructions to the whole space.
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| 7. | Using a partition of unity the task of extending reduces to a neighbourhood of the end points of.
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| 8. | Since the sheaf of functions on a manifold admits partitions of unity, the sheaf-cohomology vanishes for.
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| 9. | This is known as the "'partition of unity "'property of the basis functions.
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| 10. | The elastic transformations respect the partition of unity, there are no holes created or surfaces counted several times.
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