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. This 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.

10 pages

References in corpus (2)

• Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces
• On homotopy types of diffeological cell complexes

Cited by in corpus (2)

• A comparison between two de Rham complexes in diffeology
• Local systems in diffeology