The Locally Flat Approximation of Cell-Like Embedding Relations

Abstract

By means of M.A. Stan'ko's clever unknotting technique we show that every embedding f: Mn' -> N (n > 5) from a topological (n-l)-manif old Mn-l into a topological n-manifold N can be approximated by locally flat embeddings. A serious technical difficulty forces us to work in the category of cell-like embedding relations rather than single-valued embeddings. The bonus of this enforced generality is that the results obtained will surely have application to the study of cell-like decompositions and generalized manifolds.