WHITNEY APPROXIMATION FOR SMOOTH CW COMPLEX

Abstract

We show a Whitney approximation theorem for a continuous map from a manifold to a smooth CW complex, which enables us to show that a topological CW complex is homotopy equivalent to a smooth CW complex in a category of topological spaces. It is also shown that, for any open covering of a smooth CW complex, there exists a partition of unity subordinate to the open covering. In addition, we observe that there are enough many smooth functions on a smooth CW complex.