frontier of class $C^{1}$. Studying the Divergence Theorem (Gauss theorem), found the definition of frontier of class $C^{1}$. Which means? That is, the one which is a set with boundary of class $C^{1}$? Can give reference books. grateful

An explanation in more elementary terms: an open set $A$ has boundary of class $C^1$ if for every point $p$ on the boundary of $A$ there exist:

* a function $f$ of $n-1$ variables, with continuous first-order derivatives
* a number $r>0$
* an invertible linear transformation $T:\mathbb R^n\to\mathbb R^n$



such that $A\cap \\{x:|x-p|f(u_1,\dots,u_{n-1})\\}\cap \\{x:|x-p|
Unfortunately I don't have an accessible reference for this, apart from Wikipedia article on the aforementioned manifolds.