Repairing embeddings of -cells with monotone maps of

Author:
William S. Boyd

Journal:
Trans. Amer. Math. Soc. **161** (1971), 123-144

MSC:
Primary 54.78

MathSciNet review:
0282352

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a 2-sphere topologically embedded in Euclidean 3-space and is the unit sphere about the origin, then there may not be a homeomorphism of onto itself carrying onto . We show here how to construct a map *f* of onto itself such that is a homeomorphism of onto , and is a compact continuum for each point *x* in . Similar theorems are obtained for 3-cells and disks topologically embedded in .

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DOI:
https://doi.org/10.1090/S0002-9947-1971-0282352-5

Keywords:
Wild sphere,
tame sphere,
monotone map,
upper semicontinuous decomposition,
crumpled cube,
repairing embeddings

Article copyright:
© Copyright 1971
American Mathematical Society