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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Taming compacta in $ E\sp{4}$


Authors: John J. Walsh and David G. Wright
Journal: Proc. Amer. Math. Soc. 86 (1982), 646-648
MSC: Primary 57N35; Secondary 57N15, 57N45, 57N75
MathSciNet review: 674098
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Abstract: A compactum $ X$ in Euclidean $ 4$-space $ {E^4}$ is shown to be tame if its projection into $ {E^3}$ is $ 1$-dimensional and if $ \dim L \cap X \leqslant 0$ for each vertical line $ L$ in $ {E^4}$. An essential ingredient is the result due to J. L. Bryant and D. L. Sumners that a $ 1$-dimensional compactum in a $ 3$-dimensional hyperplane of $ {E^4}$ is tame in $ {E^4}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0674098-9
PII: S 0002-9939(1982)0674098-9
Keywords: Tame embeddings, topological embeddings of compacta, $ 4$-dimensional Euclidean space
Article copyright: © Copyright 1982 American Mathematical Society