Before revision:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary .
After revision:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} and closed ( i.e. M is a compact manifold without boundary .