Vol. 76, No. 1, 1978

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Special approximations to embeddings of codimension one spheres

Robert Jay Daverman

Vol. 76 (1978), No. 1, 21–32

Ancel and Cannon have shown that every embedding of an (n 1)-sphere in the n-sphere Sn can be approximated by locally flat embeddings. Here it is shown that any such embedding can be approximated by locally flat embeddings, the images of which are contained, for the most part, in a preassigned complementary domain of the original. In addition, the paper explores conditions implying the existence of better approximations possessing various properties suggested by high dimensional analogy with the conclusions of Bing’s 3-dimensional Side Approximation Theorem.

Mathematical Subject Classification 2000
Primary: 57N15
Received: 22 April 1977
Revised: 29 July 1977
Published: 1 May 1978
Robert Jay Daverman