Why?
Consider a set \(X⊂ℝ^n\); then a function \(f:X→ℝ\) is said to be $C^r$/-smooth in the sense of Whitney/ if there exist functions \(f_α:X→ℝ\), where α is a multi-index so that the appropriate Taylor expansion holds on \(X\)
Consider a set \(X⊂ℝ^n\); then a function \(f:X→ℝ\) is said to be $C^r$/-smooth in the sense of Whitney/ if there exist functions \(f_α:X→ℝ\), where α is a multi-index so that the appropriate Taylor expansion holds on \(X\)