Generalized normal bundles for locally-flat imbeddings

The objective here is to prove a Whitney Duality Theorem in the topological (nondifferentiable) situation, thus giving the dual classes a geometric interpretation in terms of an appropriate "normal bundle" associated with "locally flat" imbeddings of the topological manifold M in an (n + k) -manifold S. We construct first a theory of Stiefel-Whitney classes for topological manifolds (not necessarily compact or triangulable) using essentially the tangent space of Nash [10]. We then associate to every "locally flat" imbedding M C S a "normal fiber space" and prove the Whitney Duality Theorem in this setting. We include also a proof of Wu's