Special approximations to embeddings of codimension one spheres

Robert Jay Daverman

Vol. 76 (1978), No. 1, 21–32

DOI: 10.2140/pjm.1978.76.21

Abstract

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

Milestones

Received: 22 April 1977

Revised: 29 July 1977

Published: 1 May 1978