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

Implementing an idea due to John Baez and James Dolan we define new invariants of Whitney stratified manifolds by considering the homotopy theory of smooth transversal maps. To each Whitney stratified manifold we assign transversal homotopy monoids, one for each natural number. The assignment is functorial for a natural class of maps which we call stratified normal submersions. When the stratif...