Extendedly differentiable submanifolds (Q1390372)

The zero set \(N(A)\) of an arbitrary \(\mathcal{C}^r\) operator \(A:X\rightarrow Y\) between Banach spaces is not, in general, a differentiable submanifold of \(X\). The author enlarges the notion of differentiability such that this set always becomes a differentiable submanifold in the extended sense.