Vol. 51, No. 2, 1974

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Approximating polyhedra in codimension one spheres embedded in sn by tame polyhedra

Robert Jay Daverman

Vol. 51 (1974), No. 2, 417–426

We investigate properties of an (n1)-sphere Σ topologically embedded in the n-sphere Sn(n 6) implying that each (n3)-dimensionaI polyhedron in Σ can be homeomorphically approximated by polyhedra in Σ that are tame in Sn. In case Σ bounds an n-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.

Mathematical Subject Classification
Primary: 57C55
Secondary: 57A45
Received: 5 January 1973
Published: 1 April 1974
Robert Jay Daverman