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A
two sided approximation theorem for 2-spheres
William Thomas Eaton |
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Vol. 44 (1973), No. 2, 461–485
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Abstract |
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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
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Milestones
Received: 28 September 1971
Revised: 28 June 1972
Published: 1 February 1973
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Authors |
| William Thomas Eaton | |
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