| 1. | It is also clear that uniform convergence implies local uniform convergence.
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| 2. | It is also clear that uniform convergence implies local uniform convergence.
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| 3. | It is easy to see that local uniform convergence implies pointwise convergence.
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| 4. | This approach justifies, for example, the notion of uniform convergence.
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| 5. | By Morera's theorem we have a uniform convergence:
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| 6. | The resulting topology is the topology of local uniform convergence ."
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| 7. | This criterion for uniform convergence is often useful in real and complex analysis.
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| 8. | Uniform convergence implies pointwise convergence and uniform Cauchy convergence.
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| 9. | This theorem does not hold if uniform convergence is replaced by pointwise convergence.
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| 10. | This is the Cauchy criterion for uniform convergence.
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