Whitney's and Seeley's type of extensions for maps defined on some Banach spaces

Victoria Rayskin

Let $X=C[0,1]$, and $Y$ be an arbitrary Banach space. Consider a collection of open segments $\{V_i\}\subset X$. Suppose the map $f:{\cup }_i{V}_i\to Y$ has $q$ bounded Fréchet deri…