21. In this example one can easily see that pointwise convergence does not preserve differentiability or continuity. 22. As far as I know, having continuous partial derivatives is strictly a stronger condition than differentiability . 23. All functions are assumed to be of differentiability class " C " 1 unless otherwise noted. 24. One notion of continuous differentiability in " U " requires that the mapping on the product space 25. The problem is that we are talking about exponentials, rather than the differentiability of a constant function. 26. Finally, since differentiability implies continuity, the contrapositive states " discontinuity " implies non-differentiability. 27. Finally, since differentiability implies continuity, the contrapositive states " discontinuity " implies non-differentiability . 28. Space is by definition a continuum, but the assumption of differentiability is not supported by any fundamental reason. 29. The Riesz transforms arises in the study of differentiability properties of harmonic potentials in potential theory and harmonic analysis. 30. The assumption of differentiability can be weakened to continuity and one-sided differentiability of " f ".
