Approximating polyhedra in codimension one spheres embedded insnby tame polyhedra
Robert J. Daverman · Pacific Journal of Mathematics · 1974
We investigate properties of an (n -1)-sphere Σ topologically embedded in the w-sphere S n (n ^ 6) implying that each (n -3)-dimensional polyhedron in Σ can be homeomorphically approximated by polyhedra in Σ that are tame in S n .In case Σ bounds an w-cell, we relate these properties and the existence of homeomorphic approximations to Σ by locally flat spheres "mostly" outside this n-cell.This leads to a negative result eliminating a natural generalization to Bing's Side Approximation Theorem. 1Φ Definitions and notation. For any point p in a metric space