A simple triangulation method for smooth manifolds
Stewart Scott Cairns · Bulletin of the American Mathematical Society · 1961
We first triangulate a compact closed m-manifold M of differentiability class C (r>l) in a euclidean space = E. The method is simpler than earlier methods (see References) and is applicable to a wider class of spaces (see (F) and (G) below). (A) For a given rj>0, let (#i, • • • , aM) be a set of distinct points on M such that each point of M is at distance <rj from at least one point a*. Let d be the euclidean distance function in E For each * G ( 1 , • • • ,M),let