Vol. 22, No. 2, 1967

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Simplifying intersections of disks in Bing’s side approximation theorem

Frederick M. Lister

Vol. 22 (1967), No. 2, 281–295

In Bing’s Side Approximation Theorem for 2-spheres in Ea the disks on the approximating sphere and the disks on the given sphere may intersect in a very complicated manner. It is shown in this paper that the disks may be chosen so that there are the same number of disks on the approximating sphere as on the given sphere and the disks intersect in a one-to-one fashion. Furthermore, the approximating homeomorphism may be chosen so that it maps each disk on the given sphere onto the disk on the approximating sphere which it intersects.

Applications are given to a study of the preservation of tameness of subsets of the boundary of a crumpled cube under re-embeddings of the crumpled cube in E8.

Mathematical Subject Classification
Primary: 54.78
Received: 3 June 1966
Published: 1 August 1967
Frederick M. Lister