Vol. 44, No. 2, 1973

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A two sided approximation theorem for 2-spheres

William Thomas Eaton

Vol. 44 (1973), No. 2, 461–485

The side approximation theorem proved by R. H. Bing and later improved by F. M. Lister states that a sphere S topologically embedded in Euclidean three space can be 𝜖 approximated with polyhedral spheres g(S) and h(S) such that g(S −∪Gi) Int S,g(Gi) S Gi,h(S −∪Hi) ExtS, and h(Hi) S Hi where {Gi} and {Hi} are respectively finite collections of disjoint 𝜖-disks in S. In this article the theorem is strengthened by showing that the sets Gi and Hi may also be taken to be disjoint.

Mathematical Subject Classification
Primary: 55A35
Received: 28 September 1971
Revised: 28 June 1972
Published: 1 February 1973
William Thomas Eaton