| 11. | All polynomials are holomorphic functions which is a very strong condition regarding differentiability.
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| 12. | Exist and are continuous for all in the domain, has differentiability class.
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| 13. | One can classify functions by their "'differentiability class " '.
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| 14. | Roughly speaking, differentiability puts a bound on how fast the curve can turn.
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| 15. | It is also related to a completely general definition of differentiability given by Carath�odory.
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| 16. | In particular, continuous differentiability of " f " need not be assumed.
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| 17. | These criteria of differentiability can be applied to the transition functions of a differential structure.
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| 18. | Fr�chet differentiability is a strictly stronger condition than G�teaux differentiability, even in finite dimensions.
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| 19. | Fr�chet differentiability is a strictly stronger condition than G�teaux differentiability, even in finite dimensions.
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| 20. | The open mapping theorem points to the sharp difference between holomorphy and real-differentiability.
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