An example of a wild -sphere in in which each -complex is tame

Author:
J. L. Bryant

Journal:
Proc. Amer. Math. Soc. **36** (1972), 283-288

MSC:
Primary 57A15

MathSciNet review:
0319202

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Abstract: The main purpose of this note is to give an example promised in the title (for ). The example is the *k*-fold suspension of Bing's 2-sphere in in which each closed, nowhere dense subset is tame. Our efforts were motivated by recent results of Seebeck and Sher concerning tame cells in wild cells and spheres. In fact, we are able to strengthen one of Seebeck's results in order to prove that every embedding of an *m*-dimensional polyhedron in our wild -sphere can be approximated in *S* by an embedding that is tame in .

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DOI:
https://doi.org/10.1090/S0002-9939-1972-0319202-0

Keywords:
Tame embedding,
wild embedding,
1-ULC

Article copyright:
© Copyright 1972
American Mathematical Society