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