The locally flat approximation of cell-like embedding relations


By means of M.A. Štan’ko’s clever unknotting technique we show that every embedding $f: M^{n-1} \to N^n (n\ge 5)$ from a topological $(n-1)$-manifold $M^{n-1}$ into a topological $n$-manifold $N^n$ 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.


Fredric D. Ancel

James W. Cannon