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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Wild cells in $E^{4}$ in which every arc is tame


Author: Robert J. Daverman
Journal: Proc. Amer. Math. Soc. 34 (1972), 270-272
MSC: Primary 57A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0295312-1
MathSciNet review: 0295312
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Abstract: Seebeck has proved that if an m-cell C in Euclidean n-space ${E^n}$ factors k-times, $m \leqq n - 2$, and $n \geqq 5$, then every embedding of a compact k-dimensional polyhedron in C is tame relative to ${E^n}$. We prove the analogous result for $n = 4$ and $m \leqq 3$.


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Keywords: Tame embedding, wild cell, <!– MATH $\varepsilon$ –> <IMG WIDTH="15" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\varepsilon$">-push, 1-ULC, factored cell in <IMG WIDTH="33" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${E^n}$">
Article copyright: © Copyright 1972 American Mathematical Society