Whitney Embedding Theorem

Abstract

This is the smallest chapter of this book, because it contains only two theorems which are due to Whitney. These theorems have three serious reasons to study. Firstly, in its proof, the celebrated Sard’s theorem got an application. Secondly, the statement of Whitney embedding theorem was contrary to the common belief that a smooth manifold may not have any ambient space. Thirdly, in its proof, Whitney used almost all tools of smooth manifolds developed at that time. Fortunately, in this chapter, we have all the prerequisite for its proof in the special case of compact smooth manifolds. For the general case, which is more difficult, one can find its proof somewhere else.